MSc Thesis. Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria

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1 MSc Thesis Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Robbert Drieman June 8, 2011

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3 MSc Thesis Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Delft University of Technology Faculty Civil Engineering & Geosciences Hydraulic Engineering Section Graduate student Robbert Drieman Student number: Graduation committee Prof.dr.ir. M.J.F. Stive (TU Delft, Hydraulic Engineering) Ir. H.J. Verhagen (TU Delft, Hydraulic Engineering) Dr.ir. M. Zijlema (TU Delft, Environmental Fluid Mechanics) Eng. B.V. Savov (B.V.S. Consult Ltd.) Graduation date June 8,

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5 Preface This report is the final result of my master thesis. The title of the report is Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria. With this master thesis I finish my study of Civil Engineering at Delft University of Technology in the graduation specialisation Coastal Engineering. Part of the graduation period I spend in Bulgaria. I would like to thank the members of my graduation committee for their assistance during my master thesis. Furthermore, my gratitude goes to my family and friends who supported me during my study period. Robbert Drieman Delft, June

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7 Abstract The coast of Bulgaria is subject to erosion. Because of this fact, around the town of Balchik, which is situated on the Black Sea coast, almost no sandy beaches are present. Last years there have been vast tourist developments in and around Balchik. Because of these developments, the province demands solutions to adapt coastal protection structures to become more attractive regarding recreation. In this study, a small pilot project on the creation of an artificial beach will be described. One possible source of nourishment sand is to dredge it from the local bottom. However, this sand is too fine to form a stable beach without a breakwater in front of it for protection. In this study is investigated whether it is technically feasible to use a floating breakwater to protect the new proposed beach in Balchik. In order to do this, the following approach is followed. A description of the current situation as well as boundary conditions regarding wind, waves, water level, bathymetry and sediment properties is given. Next, the maximum allowed wave height to form a stable beach is determined by means of sediment transport calculations in cross-shore and longshore direction and several possible nourishment sand sizes are considered. In order to lower the incoming waves (boundary conditions) to the maximum allowed wave conditions, a floating breakwater with a certain transmission coefficient is necessary. An investigation on possible types of floating breakwaters is made and the possibilities to produce the floating breakwater are described. From the types of breakwaters found, the most suitable type is selected. The last step is to determine the required dimensions and offshore distance of the floating breakwater in order to achieve the required transmission coefficient. If the required dimensions stay within reasonable limits, it can be concluded that it is technically feasible to use a floating breakwater as beach protection. It is chosen to use concrete caissons to create the floating breakwater, because of the fact that in the vicinity of the project location a company is located which can produce floating concrete structures. Regarding beach nourishment materials, the equilibrium beach profiles with mean grain diameters 0.1, 0.2 and 1.0 mm are considered. It is chosen to further elaborate the case of the locally available sand with a mean grain diameter of 0.1 mm, because for this sand a floating breakwater is necessary in order to stabilize the nourishment. The other two sediment sizes may form a stable beach without a breakwater in place. In order to determine the required dimensions of the floating breakwater, a distance of 200 m between the floating breakwater and the coastline is chosen. With the aid of a literature study on floating breakwater dimensions it is found that for this particular location and governing wave conditions, the draft of the floating breakwater is the governing parameter which determines the transmission coefficient. The breadth of the structure is determined by stability requirements. In this design, it is assumed that the breakwater is fixed in space, which is, regarding the main outline of the design, a reasonable assumption. The result of the study is a preliminary design of a beach nourishment with a volume of 91,000 m 3 which is protected by a 240 m long floating breakwater consisting of three elements. The final conclusion of this study is that it is technically feasible to use a floating breakwater as beach protection measure. 7

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9 Contents Preface... 5 Abstract... 7 Chapter 1 Introduction Problem description General Objectives Approach Final result of study Chapter 2 Current situation of the project location Coastal erosion in Bulgaria Current situation History Description of the project location Chapter 3 Environmental and physical conditions Bathymetry Bathymetry of the Black Sea Global bathymetry Detailed bathymetry (2005) Bathymetric survey Wind Wind systems governing the Black Sea Wind data Storm duration Water level Tidal water level variation Wind set-up Conclusion Currents Offshore wave climate Gloria drilling platform ARGOSS database Evaluation of sources Calculation of wave climate at the project location General problem description Wave directions Wave climate at a depth of 50 m (offshore) Cape Kaliakra (northeast) SwanOne: shoaling, refraction, breaking, bottom friction (east, southeast and south) Sediment properties Sediment properties of sand near revetment Sediment properties of sand used for nourishment Field research Results of laboratory analysis Conclusions Chapter 4 Required wave conditions Introduction Laboratory research on beach erosion control by a submerged floating breakwater Prototype experiments on floating structures in Lake Grevelingen, The Netherlands Longshore sediment transport, theoretical background

10 4.2.1 CERC formula Formula of Kamphuis Choice of longshore transport formula Longshore sediment transport, application of theory Longshore sediment transport formula by Kamphuis Input wave climate Longshore sediment transport calculation for current situation Results: yearly longshore sediment transport quantities Remarks Sea breeze effect Blocking effect of groynes Conclusion Cross-shore sediment transport, theoretical background Bruun Dean Closure depth Vellinga Beach nourishment Cross-shore sediment transport, application of theory Current situation New situation Conclusions General conclusions Distance to coastline Chapter 5 Wave transmission coefficient and floating breakwater type Wave transmission coefficient Design value Distinction between summer and winter wave conditions Suitable types of floating breakwaters Types of floating breakwaters from literature Local production possibilities Choice of type of floating breakwater Chapter 6 Interaction between floating breakwater and beach First assumptions Transmission coefficient Global dimensions of cross-section Transmission coefficient in literature Design parameters Choice of design method and determination of required dimensions Problem description Mooring forces and mooring system Possible mooring systems Mooring forces Choice of suitable mooring system Plan form considerations Currents behind the breakwater Water quality Chapter 7 Preliminary design Chapter 8 Conclusions and recommendations Conclusions General conclusion Sub-conclusions Recommendations Recommendations for follow-up studies Recommendations regarding construction References

11 Figure references Appendix A Bathymetry survey Appendix B Wind set-up calculation Appendix C Wave climate C.1 Offshore wave climate C.2 Near shore wave climate Appendix D Sediment sample analysis D.1 Field research D.2 Method to determine sieve curves D.2.1 Scope of the test D.2.2 Equipment used D.2.3 Preparations D.2.4 Scale calibration of the hydrometer D.2.5 Execution of the test D.2.6 Density measurements D.2.7 Calculation D.3 Results regarding sieve curves D.3.1 Near shore samples D.3.2 Offshore samples D.3.3 Offshore samples D.4 Determination of amount of calcium carbonate D.4.1 Method D.4.2 Results D.4.3 Laboratory report (in Dutch) Appendix E Sediment fall velocity calculation Appendix F Longshore transport calculation Appendix G Calculation of breaker depth and refraction Appendix H Visit Ship Machine Building Appendix I Types of floating breakwaters I.1 Classification of floating breakwaters I.2 Types of floating breakwaters I.2.1 Reflective types I.2.2 Dissipative types I.3 Further reading Appendix J Breakwat calculations of overtopping and required freeboard J.1 Overtopping and required freeboard J.2 Wave force Appendix K Calculation amount of available sand

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13 Chapter 1 Introduction The subject of this MSc thesis will be the protection of a new to be created artificial beach in the town of Balchik in Bulgaria. At this moment, not many beaches are present in Balchik. However, in the last years, a lot of hotel development has been observed along the coast. To make the coast more attractive for tourism, the development of artificial beaches along the coast might be interesting. In 2005, a preliminary works design has been made by Eng. B. Savov of the Black Sea Coastal Association (SAVOV, 2005). In this preliminary design it was proposed to protect the new beach by means of a submerged breakwater. However, the idea came up that a floating breakwater might be a more attractive solution, in view of both the costs and the environment. The feasibility on the use of a floating breakwater for beach protection will be investigated in this report. 1.1 Problem description General Balchik is a town in the northeast of Bulgaria situated on the Black Sea coast, see Figure 1.1. It is situated in the province of Dobrich. Balchik is situated approximately 30 km northeast of the city of Varna. Last years there have been vast tourist developments in and around Balchik. Because of these developments, the province demands solutions to adapt coastal protection structures to become more attractive regarding recreation. The presence of beaches along a coast is attractive for tourists. However, beaches are lacking around Balchik. Figure 1.1: Location of Balchik in Bulgaria, indicated with red rectangle (GOOGLE MAPS, 2010). In this study, a small pilot project regarding the creation of an artificial beach will be described. In SAVOV (2005) a preliminary works design regarding this pilot project has been made. The project location is situated just west of Balchik, see Figure

14 It is proposed to create an artificial beach along a 200 m long stretch of coast in front of the existing revetment. In Figure 1.3 an impression is given of the proposed beach. It is expected that a protection will be necessary to shelter the beach from incoming waves to reduce erosion. In SAVOV (2005) a submerged breakwater as wave attenuator is proposed. However, this idea was not implemented because of financial reasons. A better idea might be the implementation of a floating breakwater instead of the proposed submerged breakwater. A floating breakwater has the advantages that it is more environmental friendly and probably cheaper to construct. Another disadvantage of a submerged breakwater is the necessity to apply for a construction permit, which is a time and money consuming job in Bulgaria. The advantage of a floating breakwater is that only a mooring permit is needed, which is easier to obtain. In this report, the feasibility of the use of a floating breakwater to protect the beach against erosion will be elaborated further. Balchik Cape Kaliakra 10 km N Balchik Location of proposed beach Marina Port N 100 m Figure 1.2: Project location (GOOGLE EARTH, 2010 and BING MAPS, 2010). 14

15 Proposed artificial beach Figure 1.3: Artist impression of the proposed artificial beach, view towards the west (SAVOV, 2005) Objectives Taking into account the above descriptions, the main objective of this study can be formulated as follows: - Investigate whether it is technically feasible to use a floating breakwater to protect a new artificial beach in Balchik, Bulgaria. This main objective can be subdivided in two sub-objectives: - Make a functional design for a floating breakwater to protect the artificial beach. The position and the global dimensions of the breakwater will be determined. The functional design will include features as a calculation of the mooring forces and the selection of an appropriate mooring system. - Check if the beach is actually stable under the occurring wave conditions, with the designed breakwater in place Approach Next, a number of steps is listed that will be followed to achieve the above mentioned objective. These steps will be elaborated more in detail in the following chapters. Between brackets will be indicated in which chapter(s) the step will be elaborated. Step 1: Step 2: Step 3: Describe the current situation of the project location and describe the processes (natural and human intervention) that made the project location as it is now (Chapter 2). Investigate what boundary conditions occur at the location of the proposed beach (Chapter 3). Investigate what wave conditions are required for a dynamically stable beach, given the beach material grain size distribution (Chapter 4). 15

16 Step 4: Step 5: Step 6: Step 7: Determine which time of the year the breakwater is needed. Calculate the required wave transmission coefficient (Chapter 5). Make an overview of what kind of floating breakwaters are possible and available at this moment and choose the most suitable type to achieve the required transmission coefficient (Chapter 5). Determine the global required dimensions of the floating breakwater, in order to achieve the necessary transmission coefficient (Chapter 6). Further elaborate the designed breakwater, regarding mooring forces, mooring system and plan form considerations (Chapter 6). In Chapter 7 the preliminary design will be given, as a result of the seven steps mentioned above. The approach has been illustrated in Figure 1.4. Waves from open sea (on the left) will approach the coast. While travelling from deep water towards the coast, the waves will transform under the influence of processes like shoaling and refraction. The occurring wave conditions will be determined in step 2. On the right, the new to be created artificial beach has been indicated. For the creation of a dynamically stable beach, a certain maximum wave height is allowed to occur in front of the beach. This maximum allowed wave height will be determined in step 3. To achieve this maximum allowed wave height, on the place of the question mark a floating breakwater has to be designed. This breakwater should have a certain transmission coefficient, which will be calculated in step 4. On the leeside of the breakwater, a certain transmitted wave height will remain. Step 5 involves the choice of type of floating breakwater. Step 6 and 7 involve the design of the breakwater. Figure 1.4: Illustration of approach to be followed in this study Final result of study The final result of this MSc thesis will be a report in which the above mentioned steps have been elaborated. It will describe if it is technically feasible to use a floating breakwater for beach protection. The breakwater has to fulfil the requirement to prevent or reduce erosion of the new to be created artificial beach. 16

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19 Chapter 2 Current situation of the project location 2.1 Coastal erosion in Bulgaria The territory of Bulgaria can be subdivided in several geological areas. One of them is the Moesian platform, which is a relative flat area in the northern third of the countries territory. The area has a low relief with an average elevation of less then 200 m. In the west it is bounded by the edge of the continental shelf of the Black Sea. This edge is the steep underwater continental slope (FOOSE AND MANHEIM, 1975). Many landslides are mapped over the whole territory of Bulgaria. One of the factors causing landslides is cliff erosion along the Bulgarian coast. Coastal erosion is observed along approximately 70% of the length of the Bulgarian coast. The sea is washing away material from the cliffs and transports this material offshore. At a certain moment the retaining force of a cliff can be exceeded and a piece of cliff will slide down. High rates of coastal erosion are observed in the vicinity of Balchik. Another factor that is related to landslides is precipitation. BRUCHEV et al. (2007) state that there is a close relation between precipitation and the activation of landslides. Landslides activity shows higher concentration during spring. This is connected with reaching a maximum of precipitation caused by melting snow and spring rainfall. According to some publications, around Balchik, successful predictions on the activation of landslides can be made. Short-term forecasts can be made on the basis of the ground water level (BRUCHEV et al., 2007). After the seventies of the twentieth century, problems regarding coastal erosion intensified along the Bulgarian coast. This is mainly caused by human activities in the coastal zone. During three decades the amount of sediment, which comes from cliffs, river discharge and wind processes has been decreased significantly. The river sediment discharge has been decreased due to the construction of dams upstream and the supply of sediment from cliffs also decreased due to the construction of coastal protection structures. Landslides caused by erosion of cliffs are serious problems along the Bulgarian coast. As a result of these landslides, several important coastal infrastructure objects have been destroyed and land losses occurred. In the seventies and eighties of last century, several substantial coastal defence works have been constructed along the Bulgarian coast, like groynes, revetments and sea walls. These coastal structures are amongst others intended to take away the cause of these landslides, cliff erosion. A system of a series of groynes has the function to stabilise a beach that is subject to erosion due to longshore transport. In Bulgaria, during the time of construction of the groynes, it was assumed that groynes served as a general tool to control the process of cliff erosion and landslides. Most of the groynes were constructed without a proper preliminary study on the longshore sediment transport. Because of the improper selection of groynes as coastal protection, the structures are completely ineffective. Another common-used method to defend the Bulgarian coast is the creation of revetments along the coast (In the paper of STANCHEVA AND MARINSKI (2007) the structures are called dikes, but they are not comparable to the high Dutch sea dikes. They can be better described as a revetment, with the crest level about 2 m above sea level). The revetments are built as a mount of quarry run. They usually have a seaward slope of 1:1.5. This slope is meant to reduce the effect of erosion that waves can have. For the armour layer of the revetment stones or concrete armour units are commonly used. The revetments provide sufficient protection against flooding of the hinterland, but they stop the supply of sediment from the hinterland, for example erosion of cliffs. Furthermore, they reduce the attractiveness of the coast, as they hamper the access to the water. Also, depending on the local specifics of the 19

20 plan form, the revetments may cause reduction of the beach on the seaward side and subsequently, bottom scouring may occur. A popular method of coastal defence is the combined use of groynes and a revetment. In these cases, the revetment is constructed between two groynes (STANCHEVA AND MARINSKI, 2007). 2.2 Current situation History In Figure 1.2 an overview of the project location and its surroundings can be found. In the years from 1970 to 1990 a coastal protection system has been constructed in the coastal strip of Balchik, consisting of a revetment and groynes. It was expected that between the groynes natural accretion would occur. However, it was observed that the amount of accretion is far from satisfactory. It is important to understand why. Coastal erosion is not a primary factor for land sliding. However, ones the earth slides down towards the sea, the soil becomes saturated and exposed to much higher wave impact that consequently results in higher erosion rate. If there was a large sand content in the tongue of the landslide, the erosion process would have been nourishing the surf zone with beach-forming material. The luck of such material unfortunately is determined by the geological structure where clay dominates and therefore sand beaches are almost nonexistent. The process of dissolving eroded soil in the sea water takes some time. Perhaps that is why little sand gets transported to deeper water until separated from the much finer clay. Because sand was lacking, low functionality of groynes was observed and a revetment has been built along the coast in order to supplement the effect the beach would have had. About 700 m to the east of the project location a marina is situated, which is protected by a breakwater, which in fact is an extended groyne that did not serve as affective coastal protection (SAVOV, 2005). Nowadays the cliff is almost completely isolated from the sea by a continuous revetment. Small sources of sand supply can be identified in the neighbourhood of storm water runoff outlets. The present sediment transport during storms does not cause significant changes of shoreline and bottom profiles, so one may consider that a state of dynamic equilibrium has been achieved. Creation of artificial beaches will establish new conditions that will deviate from the equilibrium. That is why measures have to be undertaken to create conditions for a new state of dynamic equilibrium. The simplest one is to use coarse sand that will form suitable erosion profile. Because such material is not available in the neighbourhood one may look for some structural measures in order to reduce the wave impact thus making finer sand applicable. Because of rapid growth of tourism in resent years the municipality of Balchik started looking for options for artificial beach creation. In 2005 a pilot project was developed, see SAVOV (2005). The location of the proposed beach is situated between two existing groynes. These groynes have a length of about 120 m. The bottom in front of the coastline has a gentle slope Description of the project location In Figure 2.1 an enlargement of the aerial photo from Figure 1.2 has been displayed. It is a more detailed view of the project location. Several elements of the project location have been indicated with numbers in the picture. Figure 2.2 displays a photo with a view on the project location as seen from the land. The view direction is southwest. In Figure 2.3 a picture with a view on the project location from sea can be found. The view direction in this picture is northeast. In Figure 2.2 and Figure 2.3 the several elements are indicated with the same numbers as in the aerial photo of Figure

21 5 4 Location of proposed beach Balchik 100 m N Figure 2.1: Aerial photo of the project location (GOOGLE EARTH, 2010). Numbers 1 and 2 indicate two groynes, one in the east and one it the west. An image of the east groyne can be found in Figure 2.4. The groynes are made of concrete and have vertical walls over the entire water depth. In between these two groynes is the location of the new proposed beach. Along the coast there is a revetment consisting of so-called tetraeders, a type of concrete armour unit. This revetment is indicated with number 4. A more detailed image of the revetment can be found in Figure 2.5. Along the coast there is a road, indicated with number 5. Between the revetment and the road, there is a sea wall. The level of the road is approximately 2 m above Black Sea level. In the northwest corner of the project location, a very small beach is present. This beach is indicated with the number 3. Pictures of this beach can be found in Figure 2.6. Near the shoreline, some rocks are present on the bottom. 21

22 4 1 2 Figure 2.2: View on the project location from sea Figure 2.3: View on the project location from land. 22

23 Figure 2.4: The groyne east of the location of the proposed beach. Figure 2.5: The revetment consisting of concrete elements called tetraeders. 23

24 Figure 2.6: In the northwest corner of the project location is a very small beach. 24

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27 Chapter 3 Environmental and physical conditions This chapter will involve the environmental and physical conditions that will affect the design of the floating breakwater. Several aspects will be elaborated in this chapter. The bathymetry will be determined (Section 3.1). Boundary conditions regarding wind (Section 3.2) and waves (Sections 3.5 and 3.6) will be determined. Other hydraulic boundary conditions as the water level (Section 3.3) and currents (Section 3.4) have to be determined. Also the sediment properties of the local material and the nourishment material are necessary for the design of the artificial beach (Section 3.7). 3.1 Bathymetry The bathymetry is an important aspect that has to be taken into account. It is important because: - the bathymetry influences the wave properties when deep water waves travel towards the coast, into shallower water. - the depth at the project location influences the design of the floating breakwater Bathymetry of the Black Sea The Black Sea is an inner continental sea which is quite deep. At some points it is deeper then 2200 m. In Figure 3.1 a bathymetric map of the entire Black Sea has been displayed. One can see that the deep inner part doesn t have much relief. The deep water bottom gradually turns in the continental slope. The gradient of the continental slope varies from 5-10 to Most of the continental shelf is narrow (3-15 km). However, in the north-western part with of the continental shelf can reach values up to 200 km (SHUISKY, 1993). Near the project location (indicated with an arrow), the width of the continental shelf is approximately 15 km, measured from the coast until the 100 m depth contour. Figure 3.1: Bathymetric map of the Black Sea. Depths in m below mean sea level (adapted from SHUISKY, 1993). 27

28 3.1.2 Global bathymetry In Figure 3.2 a bathymetric chart of the surroundings of the project location has been displayed. The project location has been indicated with an arrow. As can be seen from this chart, the depth in front of the project area gently gets larger towards the southeast. This continues until the 100 m depth contour. This depth contour lies at a distance of approximately 50 km to the south east of the project location. From the 100 m depth contour further to the south east, the bottom slope and depth increase rapidly. The depth increases until a value of approximately 2000 m. Figure 3.2: Bathymetric map of the surroundings of the project location. Depth in m below mean sea level (THEMAP, 2005). If one follows the 20 m depth contour, one sees that at a point approximately 15 km southeast of Varna the depth contour goes in northern direction. If one follows this depth contour further, at a point 10 km southeast of Balchik, one turns in southern direction again. This line indicates an elongated local depression in the sea bottom which runs along the coast between Varna and Cape Kaliakra Detailed bathymetry (2005) In SAVOV (2005) a more detailed bathymetric map of the project location can be found, see Figure 3.3. The location of the artificial beach has been indicated with a yellow dot. As can bee seen, the slope of the bottom in front of the new beach is quite gentle. The further one gets offshore, the more gentle the slope gets (the distance between the depth contours increases). Between the tips of the groynes next of the location of the beach, the depth is between 3 and 4 m. 28

29 Figure 3.3: Detailed bathymetric map of the project location. Unit along axes and depth unit: m (SAVOV, 2005) Bathymetric survey In Bulgaria, more detailed bathymetry has been obtained during a field investigation at September 14 and 15, The working method has been described in Appendix A. With the computer program Surfer 8, two bathymetric maps have been created. One map is an overview map of the surroundings of the project location. The second one is a more detailed map of the project location. The large overview map has been displayed in Figure 3.4. This map will be used for the calculation of the near shore wave climate in front of the project location. Depth contours outside the area with groynes are almost parallel. It should be noted that the west and east edges of the map are not so convenient. One would expect almost smooth and almost straight parallel depth contours. This is due to different data sources in the middle and at the edges. In the middle of the map the data source is the bathymetric survey. Because data was lacking near the edges of the map, the data set was supplemented with data from the bathymetric survey from Savov (2005). However, this is not a problem, because the main purpose of this map is to get a bottom profile to calculate the near shore wave climate. This profile will be situated in the middle of the map, so it will only cover the recent bathymetric data. 29

30 Location of proposed beach Figure 3.4: Bathymetric overview map. Depths in m with reference level Black Sea level and UTM coordinates along axes in m. The detailed map has been displayed in Figure 3.5. As can be seen, in the northwest corner of the project location, a sort of erosion hole is present. Furthermore, for depths larger then 1.5 m, the distance between the depth contours is almost equal. This indicates an almost constant bottom slope in that area. This map will be used to take cross-shore profiles to determine the maximum allowed wave conditions regarding cross-shore sediment transport. It will also be used to design the floating breakwater itself (regarding position and global dimensions). 30

31 Figure 3.5: Depths in m with reference level Black Sea level and UTM coordinates along axes in m. In both maps one can observe a steep slope near the edges of the groynes. However, in reality these slopes are not present. The groyne edges are vertical walls until the bottom. 31

32 3.2 Wind In this section, wind characteristics in the Black Sea in general will be described. Wind systems governing the Black Sea in different parts of the year will be described. This is important for the understanding of the different occurring wave heights, periods and directions in several parts of the year Wind systems governing the Black Sea The wind patterns in the Black Sea region are influenced by seasonal changes in atmospheric pressure patterns over the adjacent lands of Europe and Asia. Especially during the October-March period, the region is frequented by eastward travelling depressions. Two main tracks of winter storms can be identified: from the Mediterranean Sea in northeastward direction over the Sea of Marmara, and from Romania and Bulgaria in eastward and southeastward direction. Approximately 30 depressions per year arrive from the central Mediterranean area in the Black Sea region (Reiter, 1975 referred in ÖZSOY AND ÜNLÜATA, 1997). Figure 3.6: Overview map of the Black Sea (GOOGLE MAPS, 2010). The topography around the Black Sea influences the atmospheric flows and the passage of cyclones into the Black Sea region. The low lying area of the Sea of Marmara (see Figure 3.6) acts as a gap between mountain ridges west and south of the Black Sea. This gap allows the passage of cyclones (depressions). The land north of the Black Sea is flat and does not restrict air flows, which means that cold outbreaks can reach the Black Sea from the north. This happens especially when a persistent high pressure system is located near the Balkans (Brody and Nestor, 1980 referred in ÖZSOY AND ÜNLÜATA, 1997). In winter, wind conditions over the Black Sea are variable. In the western part, during winter, the governing wind direction is north to northeast (ÖZSOY AND ÜNLÜATA, 1997). 32

33 In MAHERAS et al. (2009) a description is given of atmospheric circulation types associated with storms on the Romanian Black Sea coast. This description could also be used for the project described in this MSc thesis, because the project location is situated just 50 km south of the Romanian border. In the paper a method of automatic classification of atmospheric circulation types is being described. Circulation types related to storms have been identified. A situation is called a storm if the occurring wind speed is higher than 12 m/s for at least 12 consecutive hours and a sea state higher than 4 near the shore occurs. Sea states are explained at a website of the military base Fort Eustis in the US (FORT EUSTIS, 2011). On this website is mentioned that a sea state higher than 4 means that a wind speed higher than 18 knots (= 9.26 m/s) and a significant wave height higher than 6 feet (= 1.83 m) occur. This means that there is an inconsistency in the paper of MAHERAS et al. (2009). On the one hand, a wind speed higher then 12 m/s is mentioned as limit to call a situation a storm, on the other hand, the sea state higher then 4 indicates that a storm old be a situation with a wind speed higher then 9.26 m/s. From the paper doesn t become clear what wind speed has been used as threshold value. Atmospheric pressure data from the period have been used. As a result of the study, 12 circulation types have been identified which influence storms along the Romanian coast. Amongst these 12 circulation types, 5 anticyclonic types (system turning clockwise) and 7 cyclonic types (anticlockwise) have been identified. Main conclusions that could be drawn regarding storms on the Romanian coast are: - The main cause of storms in the western Black Sea is a combination of an anticyclone which is generally located in the north and a depression (cyclone) in the south, from Mediterranean origin. - Most of the storms (80.3%) that occurred during the study period are related to 4 cyclonic circulation types, whose centre is located southwest, southeast or northeast of the study area. - The cyclonic type with the highest frequency of occurrence (24.5%) is the type with its centre southeast of the study area. This circulation type causes winds blowing from the northeast. - The cyclonic type that seems to cause the most severe storms is the type with its centre west southwest of the study area (frequency of occurrence of 16.9%). This circulation type causes winds blowing from the south. - Only during 18.4% of the occurring storms, an anticyclonic circulation type is involved Wind data Galata drilling platform In a study done by SLABAKOVA et al. (2009) wind data recorded at an offshore drilling platform called Galata are used. This platform is located approximately 30 km southeast of Varna (see Figure 3.8). The coordinates of the location are: 43 2'32"N and 28 11'27"E. The water depth at the location of the platform is 34 m. Wind data are recorded by an anemometer which is placed at a height of 26 m above the sea surface. Wind rose plots based on the in situ measured wind data from 2007 are given in Figure 3.7. As can be seen from Figure 3.7a, during January and February (winter 2007) winds from the northeastern sector prevailed. From Figure 3.7b one can see that during June and July (2007) light winds from the northwestern sector prevailed. Also some light winds from the southeastern sector occurred. 33

34 Figure 3.7: Wind roses from Galata platform measurements for January-February (a) and June-July (b) in Colours indicate wind speeds in m/s (SLABAKOVA et al. 2009). Figure 3.8: Locations of wind data sources (GOOGLE EARTH, 2010). 34

35 Windfinder Cape Kaliakra Regarding wind statistics, data from a wind station at Cape Kaliakra can be found at WINDFINDER (2010). The location of the wind station can be found in Figure 3.8. Yearly wind statistics can be found in Figure 3.9 for Cape Kaliakra. As can be seen from Figure 3.9, during the time between March 2008 and May 2010, the main wind direction was north northeast. Other, less important directions are northwest and southwest. However, the dominant wind direction during the months April to September, is north. During the winter months November to March, the prevailing wind direction is northwest. Figure 3.9: Wind statistics from measuring station at Cape Kaliakra (WINDFINDER, 2010). At WINDFINDER (2010) wind statistics for the station at Cape Kaliakra are also available per month. ARGOSS database The main source of data regarding wind and waves that will be used during this study will be a database owned by BMT ARGOSS. BMT ARGOSS operates a regional third generation wave model of the Black Sea. The model provides 3-hourly time series of wave spectra. These data cover a period of at least 16 years. Satellite observations regarding wave height and wind speed are used to calibrate the models (ARGOSS, 2010). Regarding wind information, the following data are available from the ARGOSS database. What should be kept in mind using these data, is that some of the datasets are not based on one output point, but on an area of 50 x 50 km. The area and its centre point (43 o 03'N, 28 o 13E) are displayed in Figure Significant wave height vs. wind speed scatter table o Data source is altimeter - Distribution of wind speed o Data in histogram table and graph 35

36 o Data source is altimeter - Wind speed vs. significant wave height scatter table o Data available per directional sector of 45 degrees o Data source is wave model (1 model point) - Monthly distribution of wind speed o Data presented in table o Data source is altimeter - Exceedance curve wind speed o Data presented in table and graph o Curve shows the significant wave height versus the fraction of time it is exceeded. o Data source is altimeter Figure 3.10: Location of ARGOSS data area of 50 x 50 km with centre point (GOOGLE EARTH, 2010) Storm duration To calculate the probabilities of exceedance of a certain wave height, which will follow in a section later in this report, an estimation of the duration of a storm that might occur near the project location is necessary. Storms along Romanian coast In a report (COMAN, 2004) on coastal erosion near the town of Mamaia in Romania, some information on storms along the Romanian coast can be found. The prevailing wind direction during storms along the Romanian coast is from the north. 80% of the storms come from this direction during a period of 20 years ( ) (Diaconu, 1994 referred in COMAN, 2004). This is a citation from the report about the duration of storms along the Romanian coast: Mean duration (about 30 hours) and maximal duration of storms (more than 130 hours) are recorded for wind from the north. A graph with the number of storms per month during the period from 1980 to 1993 can be found in Figure From this graph it becomes clear that most of the storms take place in winter. 36

37 Figure 3.11: Number of storms per month in the period between 1980 and 1993 (COMAN, 2004). The graph in Figure 3.12 shows the number of storms per year during the period from 1980 to 1993 that lasted more than 72 hours. From this graph becomes clear that in this period on average 1.7 storms occurred per year that lasted longer than 72 hours. Figure 3.12: Storm durations longer than 72 hours in the period between 1980 and 1994 (COMAN, 2004). From this report it doesn t become clear what the exact location is where the used data have been measured. Also it is not clear what wind speed is used to define the duration of a storm. Conclusion Not much information on the duration of storms along the Bulgarian coast has been found. Therefore it is assumed that a representative value for the duration of a storm along the Bulgarian coast is 30 hours. This is the mean duration of a storm as mentioned in the citation mentioned above. 3.3 Water level Tidal water level variation The Black Sea water level hardly depends on tides. This can be seen in the water level graphs shown in Figure The graphs have been adopted from a website operated by the Institute of Oceanology in Varna (IO-BAS, 2010 AND 2011). The water levels are measured with a water level gauge in the port of Balchik. The location of the tidal gauge has been displayed in Figure 3.13c. Every two minutes a water level measurement is recorded. Figure 3.13a and b display two measurement graphs, one recorded in September 2010 and one recorded in January The reference level of the gauge is not known. From the graphs, an indication of the tidal variation in the Black Sea can be obtained. 37

38 Figure 3.13: Water level measurements in the marina of Balchik (IO-BAS, 2010 AND 2011). It should be noted that the reference level of the water level gauge is unknown. The many wiggles which are observed in the record, may be caused by local effect of wind setup, waves caused by a passing ship or wind waves. From the graphs can be estimated that the tidal range will be in the order of 20 cm. This means that the tidal amplitude will be 10 cm. These values are rather low, that s why the tidal variation of the Black Sea will be neglected during this further research, as it can be assumed that the tidal variation won t influence the outcome of the investigation much Wind set-up Wind from the main wind directions east, southeast and south will cause wind setup near the project location. As mentioned in the section about wind, the main storm direction is northeast. However, because of the west-east orientation of the coastline at the project location, northeastern wind can t cause wind setup at the project location. The mains wind direction that can cause wind setup near the project location, are east (E), southeast (SE) and south (S). 38

39 Regarding wind set-up, an indicative calculation per main wind direction (E, SE and S) will be made. This will be done with the aid of the computer programme CRESS (Coastal and River Engineering Support System), amongst others developed by Delft University of Technology. The programme contains several pre-programmed formulas on several hydraulic engineering aspects. One of them is wind set-up. The programme can calculate the wind set-up in two steps, as can be seen in Figure This twostep calculation is more or less representative for the sea bottom in front of the project location. For a detailed explanation of the calculation procedure is referred to Appendix B. Figure 3.14: Calculation of wind setup (CRESS, 2010). In Table 3.1, the input and the results of the calculation can be found. The maximum wind speeds have been obtained from scatter tables retrieved from the ARGOSS (2009) database. These scatter tables can be found in Table 3.4 and Table 3.6. The fetch length has been chosen to be the distance from the 75 m depth contour to the 20 m depth contour. The width of the shallow zone is equal to the distance from the 20 m depth contour until the coastline. Wind direction Max. wind speed [m/s] Fetch length [km] Table 3.1: Wind set-up calculation. Water depth [m] Width of shallow zone [km] Depth of the shallow zone [m] Total setup [m] E SE S From the table can be read that the maximum expected wind set-up will be in the order of 0.20 m. This value is insignificant in this stage of the research. That s why wind setup will be ignored in this research Conclusion From the calculations that have been presented above, it can be concluded that in this stage of the research water level variations can be neglected. 3.4 Currents As mentioned before, tidal water level variations are negligible in the Black Sea. That s why tidal currents are also negligible. SHUISKY (1993) mentions that in the Black Sea currents are present that can be classified as wind, drift and stream currents. Their velocities are between 0.15 and 0.30 m/s. Under the influence of waves, wave driven currents are generated. During severe storms, the maximum wave velocities near Varna had a value up to 1.8 m (SHUISKY, 1993). From the types of 39

40 currents mentioned, wave driven currents contribute to sediment transport. If there is already sediment in suspension in the water column, the other currents might also contribute to sediment transport. 3.5 Offshore wave climate In this section, several sources of offshore wave data will be described. At the end, a reflection will be given if the different sources give consistent information Gloria drilling platform In RUSU (2009) measured wave data from an offshore drilling platform called Gloria are mentioned. These data give a good impression of the occurring offshore wave conditions throughout the year. The drilling platform is situated approximately 50 km east of the Romanian coast, see Figure The coordinates of the location of the platform are 44 31'N and 29 34'E. The water depth at that location is about 50 m. Figure 3.15: Location of the Gloria drilling platform (GOOGLE EARTH, 2010). In RUSU (2009) an analysis based on these measured data is given. The results of this analysis can be seen in Figure A distinction has been made between results for the entire year and results for winter time (October to March). Classes of significant wave height are given in Figure 3.16a and b. Classes of mean wave periods can be found in Figure 3.16c and d. Wave direction distributions are given in Figure 3.16e and f. The left column of these graphs corresponds to results for the whole year, the right column gives results for winter time. Monthly maximums and averages of the wave heights and wave periods are given in Figure 3.16g and h, respectively. 40

41 Figure 3.16: Analysis of the wave data measured at Gloria drilling platform in the period (RUSU, 2009). a: Classes of significant wave height (H s ) for total time interval; b: classes of H s for wintertime; c: classes of mean period T m for total time interval; d: classes of T m for wintertime; e: mean wave direction distribution for total time interval; f: mean wave direction distribution for wintertime; g: monthly averaged values for the medium and maximum wave height; h: monthly averaged values for the medium and maximum wave period. 41

42 From Figure 3.16a and b can be seen that the class distribution regarding significant wave height is almost the same during the entire year and during the winter period. Most of the waves have a height in between 1 and 2 m. Around 20% of the waves has a height in the class of 0-1 m. The classes 2-3 and 3-4 m come at the 3 rd and 4 th place, respectively. Waves higher than 4 m occur less often. In Figure 3.16c and d, wave period histograms for the entire year and winter haven been displayed. As can be seen, the distribution for the entire year and the one for winter are almost the same. About 50% of the waves have a period between 5 and 7 seconds. A little more than 40% of the waves have a period between 3 and 5 seconds. For the entire year, 5.19% of the waves occur in the class 7-9 s. During winter only, 7.45% of the waves occur in this class. Very occasionally, waves with a period between 9 and 11 seconds occur. Waves with a period longer than 11 s have not been recorded. Figure 3.16e and f show that the dominating wave direction is from the northern sector (northwest, north and northeast) both during the entire year (52.6%) as during winter (52.73%. For the entire year, 33.9% of the waves come from the southern sector (southwest, south and southeast). During winter, 35.85% of the waves come from the southern sector. As can be seen in Figure 3.16g, the monthly average maximum wave height varies between 1 and 3 m. The highest monthly maximum wave height occurs in January and is about 11 m. The lowest monthly maximum occurs in June and is about 4 m. In Figure 3.16h can be seen that the monthly average period remains almost constant between 5 and 5.5 seconds all year round. The maximum monthly wave period varies between 7 and 9 seconds. Analysis of the wave heights indicates that the highest average values are characteristic of waves coming from the northern sector. The maximum occurred average wave height coming from the northern sector was 5.36 m. For wave periods, the highest average value occurs with waves coming from the northeast. This maximum value is equal to 5.63 s (RUSU, 2009). Table 3.2 has been adopted from (RUSU, 2009). This table presents the average significant wave heights corresponding to the main direction for each month. This table indicates that the highest waves come from the northern sector (N, NE and NW) for the months September until May. During the remaining summer months, the highest waves come from the east, southeast and southwest. Table 3.2: Average significant wave heights [m] corresponding to the main directions computed for each month (data recorded at the Gloria drilling platform in the period ). The cells with the maximum value of the average significant wave height for each month have been coloured grey (RUSU, 2009). Month Direction N NE E SE S SW W NW January February March April May June July August September October November December

43 3.5.2 ARGOSS database More detailed wave data can be retrieved from the above mentioned ARGOSS database (ARGOSS, 2010). Regarding wave information, the following data are available from the ARGOSS database. It should be kept in mind that some of the datasets (altimeter) are not based on one output point, but on an area of 50 x 50 km. This area and its centre point are displayed in Figure Other data (SAR) are based on data measured in an area of 200 x 200 km. The centre point and this area have been displayed in Figure The depth at the location of this point is approximately 35 m. Other data are the result of wave model runs. The wave model point does not coincide with the chosen output point. It deviates a few km from the chosen output point and is situated in a water depth of about 50 m. - Seasonality of the significant wave height o Graph with average significant wave height and 90% confidence interval o Data source is altimeter - Distribution of significant wave height o Data presented in histogram table and graph o Data source is altimeter - Significant wave height vs. wind speed o Data presented in scatter table o Data source is altimeter - Distribution of significant wave height o Data presented in histogram table and graph o Data source is wave model - Monthly distribution of significant wave height o Data presented in scatter table o Data source is altimeter - Significant wave height vs. mean wave period scatter table o Data source is SAR o Size of area is 200x200 km - Significant wave height vs. zero crossing wave period scatter table o Data source is SAR o Size of area is 200x200 km - Significant wave height vs. wave direction scatter table o Data source is SAR o Size of area is 200x200 km - Wind speed vs. significant wave height scatter tables o Data available per directional sector of 45 degrees o Data source is wave model - Significant wave height vs. zero crossing period scatter tables o Data available per directional sector of 45 degrees o Data source is wave model - Monthly distribution of significant wave height o Data presented in table - Exceedance curve wave height o Data presented in table and graph o Curve shows the significant wave height versus the fraction of time it is exceeded. - Distribution of significant wave height o Data presented in histogram table and graph o Data source is altimeter 43

44 Figure 3.17: Location of ARGOSS data area of 200 x 200 km with centre point (GOOGLE EARTH, 2010) Evaluation of sources Above, two sources on wave information have been described. The first is the paper by RUSU (2009). Wave measurements from the Gloria drilling platform were used to analyse the governing offshore wave climate. The second one is the ARGOSS database, in which extensive wave and wind data can be found for a point offshore the coast of Varna. Next, a comparison will be made between the wave data from the Gloria drilling platform presented in Figure 3.16 and the available information from the ARGOSS wave database. - Figure 3.16a presents a histogram on significant wave height. One can compare this graph to a similar histogram as can be retrieved from the ARGOSS database. Both histograms indicate that most of the waves occur in the range between 0 and 2 m. However, the histograms indicate that in front of the coast of Varna more waves occur in the range between 0 and 1 m then in the wave class from 1 to 2 m. This is opposite for the measurements at the Gloria drilling platform. For the classes of waves higher then 2 m the trend is generally the same, but the percentages of the ARGOSS wave database are higher then the percentages from the Gloria drilling platform. - Figure 3.16e presents a graph with the wave direction distribution. These data can be compared with the directional scatter tables of significant wave height versus zero-crossing period from the ARGOSS database. For the northern direction, the value from Gloria is much higher then the ARGOSS value. This can be explained by the fact that north of the ARGOSS data point, the coastline is oriented east-west. That s why almost no waves are observed in the ARGOSS data. The general trend that most of the wave action occurs from the 44

45 northeastern sector can be observed in both data sources. Also, the smaller southern component is present in both sources. - Figure 3.16g displays monthly averaged values for the mean and maximum wave heights per month. If one compares this figure to a similar graph from the ARGOSS database, one can see that the mean wave heights are lower for the ARGOSS wave database then for the measurements from the Gloria drilling platform. The lower values for the ARGOSS database might be explained by the fact that the area in which the altimeter measurements have been taken, also covers a part of shallow water. However, the general trend of lower mean wave heights during summer can be observed in both data sources. The differences between both data sources can be explained by the fact that the data have been recorded during different time periods and because of the fact that the data have been measured at two different locations. It appears that, regardless the fact that there are some differences between the two data sources, the general trends are the same for both data sources. This means that the two data sources are more or less consistent in the data they present. Because of the fact that the ARGOSS database is more extensive then the paper by RUSU (2009), the ARGOSS database will be used as main source of information to calculate the governing wave climate at the project location. 3.6 Calculation of wave climate at the project location In this section, the offshore wave data mentioned in Section 3.3 will be transformed to the local near shore wave climate at the project location. One way to determine the local wave climate at the project location is to use deep water wave data that can be retrieved from the above mentioned ARGOSS database. These data can be transformed to local shallow water wave conditions. By means of the use of the depth charts that can be found in Figure 3.2 and Figure 3.3, some diffraction and refraction calculations can be made. A tool that can be used to do this, is the computer program SwanOne. This is a one dimensional spectral wave model that can simulate near shore waves. Also the shape of the shoreline has to be taken into account, because the project location is quite sheltered from waves coming from the northeast. Important design parameters for the floating breakwater are the occurring wave periods and connected to that the wave lengths. Because of this fact, the transformation of offshore wave lengths to near shore wave lengths has to be studied thoroughly. The shapes of offshore and near shore wave spectra have to be taken into account General problem description A general overview on how to calculate the wave transformation from offshore to the project location can be found in Figure As can be seen, the project location is situated in a small bay. Only waves from the southern sector can directly reach the project location. The site is sheltered from direct waves coming from the north-eastern sector. Cape Kaliakra provides this shelter. In the same time, the southern tip of Cape Kaliakra acts as a diffraction point. From data mentioned in Section 3.3 and scatter tables from the ARGOSS database follows that the most important wave direction is from the northeast (see Figure 3.18). Due to diffraction around Cape Kaliakra, part of the waves from this direction can reach the project site anyway. When one looks at the depth chart given in Figure 3.18, one can see that the depth contours in front of the project location are more or less parallel. To simplify the calculation process, it is assumed that the depth contours are parallel to each other. The final result of the wave climate study will be one or more graphs with the probability of exceedance versus the significant wave height and/or wave period. 45

46 The two important design parameters in this study are the significant wave height and the wave length (via the wave period). The significant wave height is important to determine the stability of the new artificial beach. The wave length is an important design parameter for the floating breakwater. Figure 3.18: Problem description (THEMAP, 2005) Wave directions Waves from the directions that can reach the project location directly are waves from the south and the southeast. The project location is sheltered from direct impact of waves coming from the north, northeast and east. However, around Cape Kaliakra diffraction will occur in case of waves from these directions. Also, because of the bottom configuration, waves coming from the east that pass south of Cape Kaliakra will reach the project location under the influence of refraction. Because of the position of the project location on the coastline, directions which are not of influence are southwest, west and northwest. Directions southeast and south First, the wave directions south and southeast will be considered. From the ARGOSS database, scatter tables per directional sector of 45 degrees can be found. The results from these scatter tables have been obtained from a wave model, with the point of output given in Figure One kind of scatter table contains information on the percentage of occurrence of the significant wave height and the zero crossing period. The tables for southeast and south have been displayed in Table

47 Table 3.3: Scatter tables with percentage of occurrence of significant wave height vs. zero-crossing wave period for the directional sectors southeast and south. Significant wave height [m] Zero-crossing period [s] total total Southeast Significant wave height [m] Zero-crossing period [s] total total South As can be seen from the tables above, the highest waves coming from the southeast and south have a significant wave height between 2 and 3 m. The corresponding significant wave period is 5-6 seconds. However, the probability of occurrence of these waves is very small, as can be seen from the percentages of occurrence. Another type scatter table contains information on the percentage of occurrence of the significant wave height and the wave direction. For the direction southeast and south, these tables can be found in Table

48 Table 3.4: Scatter tables with percentage of occurrence of wind speed vs. significant wave height for the directional sectors southeast and south. Wind speed [m/s] Significant wave height [m] total total Southeast Wind speed [m/s] Significant wave height [m] total total South From the tables above it can be seen that the wave climate from the directions southeast and south at the output point of the wave model is governed by wind sea waves. Almost all the values are located around a diagonal starting in the upper left corner. This indicates that when the wind speed becomes higher, the waves that are observed increase in height. This is typically the case with wind sea waves. The corresponding wave spectra will have a shape with only a wind sea part. Directions northeast and east The ARGOSS scatter tables with percentages of occurrence of the significant wave height and the zero-crossing period can be found in Table 3.5. The scatter tables with percentages of occurrence of the significant wave height and the wind speed are displayed in Table

49 Table 3.5: Scatter tables with percentage of occurrence of significant wave height vs. zero-crossing wave period for the directional sectors northeast and east. Significant wave height [m] Zero-crossing period [s] total total Northeast Significant wave height [m] Zero-crossing period [s] total total East From the tables in Table 3.5 it can be seen that the percentages are mainly centred around a diagonal that starts in the upper-left corner of the table. This indicates that a higher significant wave height corresponds to a longer zero-crossing period. This is typically the case with wind sea waves. However, in both tables, in the row of significant wave height 0-1 m and 1-2 m, some cells contain percentages with longer periods (up to 8-9 s). Especially for the eastern direction this is noticeable. Low wave heights with long zero crossing periods indicate the presence of swell. From these tables it can be concluded that the corresponding wave spectra will contain both a swell peak and a wind sea part. 49

50 Table 3.6: Scatter tables with percentage of occurrence of wind speed vs. significant wave height for the directional sectors northeast and east. Wind speed [m/s] Significant wave height [m] total total Northeast Wind speed [m/s] Significant wave height [m] total total East From the tables in Table 3.6 it can be seen that the values are centred around the central diagonal of the table. An obvious conclusion that could be drawn from these tables is therefore that the local wave climate from the northeast and east is governed by local generated wind sea waves. However, this is contradictory to the scatter tables in Table 3.5, from which it can be concluded that also a swell component is present Wave climate at a depth of 50 m (offshore) The depth at the location of the ARGOSS wave model output point, regarding the scatter tables from Section 3.5.2, is 50 m. Although the location of this data point is not entirely suitable to determine the local wave climate at the project location, it is assumed that the data given in the scatter tables is valid along the entire 50 m depth contour (between Varna end Cape Kaliakra). With the aid of the scatter tables with information on the joint probability of occurrence of significant wave height and zerocrossing period, a probability of occurrence graph regarding occurring wave heights has been created. The data have been grouped per direction, thereafter per significant wave height and thereafter by zero-crossing period. The upper boundaries of the classes of wave heights and periods were taken as occurring values. 50

51 Because of the fact that the data that are available are random measured values, it is not possible to use the Peak over Threshold method, to obtain an exceedance graph regarding the occurrence of storms. The following procedure has been followed: As base, the scatter tables with information about the occurrence of simultaneous values of a certain significant wave height and a certain zero-crossing period have been used. These tables can be found in Table 3.3 and Table 3.5. With the given percentages the probability of exceedance of a certain wave height has been calculated. Because of the fact that only random data are available, a certain storm duration has to be assumed, to obtain the probability exceedance distribution regarding a certain storm. In this case, a storm is defined as a period of time during which more or less the same wave height occurs. The available information regarding storm duration has been described in Section From this information was concluded that a period of 30 hours will represent the storm duration. This means that the number of storms per year N s equals: N s number of hours in a year 365 days 24 hours 292 storms per year (3.1) storm duration 30 hours The given probabilities of exceedance have been multiplied by the number of storms per year. The result can be found in a table in Appendix C.1. In Figure 3.19 (next page), the results of the calculation can be found in graphical form. The probability of exceedance has been plotted against the occurring wave heights. In Appendix C.1 the two columns that have been plotted are coloured yellow. Because of the fact that the upper boundaries of the bins from the scatter tables have been used to plot the data, the points in the graph are a bit conservative. That s why it has been decided to draw a trend line by hand, instead of using a computer programme to calculate the trend line. On purpose, the line has been drawn a bit below the points, to obtain a more realistic exceedance line. 51

52 Figure 3.19: Probability of exceedance per year of a certain storm (offshore wave climate). 52

53 Next, with the aid of SwanOne, a similar graph for the near shore wave climate will be determined Cape Kaliakra (northeast) Diffraction around Cape Kaliakra For the calculation of the diffraction around Cape Kaliakra, diffraction diagrams will be used. Wave diffraction occurs when waves encounter a structure or obstacle, in this case Cape Kaliakra. In SPM (1984a) a method presented by Wiegel in 1962 to calculate diffraction patterns behind a semi-infinite breakwater is described. For several angles of wave approach, diffraction diagrams are given. The diagrams are based on the assumption that the bottom is horizontal. The diagrams are valid for regular waves. In the diagrams lines of equal wave height reduction are given. This wave height reduction is given in terms of a diffraction coefficient K. The diffraction coefficient is defined as the diffracted wave height H diff divided by the incoming wave height H i : K ' H diff (3.2) H i The unit of distance of the diagrams is radius/wavelength, so the diagrams have to be scaled to the right size when used in wave calculations on a hydrographical chart. The wavelength L of a regular wave in arbitrary water depth can be calculated with the following expression: 2 gt 2 d L tanh 2 L (3.3) Where: L = wave length [m] g = gravitational acceleration [m/s 2 ] T = wave period [s] d = water depth [m] The value of L has to be solved iteratively. This expression is called the dispersion relationship (HOLTHUIJSEN, 2007). In Figure 3.20, the diffraction diagram for the wave direction northeast has been displayed. 53

54 Figure 3.20: Diffraction diagram for direction northeast (SPM 1984a). To get a first insight of the influence of diffracted waves on the project location, a diffraction calculation for the wave direction northeast will be. Therefore, the highest occurring wave period that can be found in the aforementioned scatter tables will be used. Further, it is assumed that the bottom between the project location and Cape Kaliakra is horizontal. The procedure is as follows. The occurring wave length will be calculated by means of Equation (3.2). Thereafter, the diffraction diagram will be scaled to the right size and overlaid on the hydrographical chart. This has been shown in Figure The diffraction diagram from Figure 3.20 has been scaled with the wave length to match the scale of the bathymetry chart in Figure This scaled diffraction diagram has been placed with its origin at the tip of Cape Kaliakra. It appeared that the scaled diagram is not large enough to extend all the way to the project location. That s why the lines of equal diffraction coefficient K from the diffraction diagram have been extended until the project location. This procedure has been illustrated in Figure

55 Figure 3.21: Diffraction calculation for direction northeast. Now, the value of the diffraction coefficient at the project location can be determined. A depth at the toe of Cape Kaliakra of 10 m has been taken. The calculation has been summarized in Table 3.7. Table 3.7: Diffraction calculation for direction northeast. Wave direction Wave period [s] Wave length [m] Diffraction coefficient K Northeast As can be seen from the results, due to diffraction only the wave heights near the project location will be reduced by a factor of 0.06 for waves from the northeast. The highest incoming significant wave height from the northeast is H i = 5 m. Consequently, the diffracted wave height will near the project location will be H K ' H m. diff i The above example calculation has been based on the highest occurring wave period. If one wants to calculate the wave reduction effect due to diffraction for incoming waves with lower wave periods, the diffraction diagram should be scaled to the right size. However, as can be seen from Figure 3.21, the scaled diffraction diagram for the highest occurring wave period is already quite small. If the diagram should be scaled for lower wave periods (and consequently lower wave lengths), it would get smaller dimensions than the one in Figure Due to this scaling, the lines of equal diffraction coefficient won t displace significantly. That s why it can be assumed that for all occurring incoming periods, the occurring diffraction coefficient near the project location is smaller than Behind Cape Kaliakra, the diffracted waves will propagate further towards the shore. They will undergo again the effects of refraction. For the to be calculated wave climate near the project location, will be assumed that the significant height of all the waves coming from the northeast will be reduced by a factor In the above described calculation, regular waves have been assumed. In reality, irregular waves will occur. In SPM (1984b) a study performed by Goda, Takayama and Suziki in 1978 has been mentioned. They have calculated diffraction diagrams for the propagation of irregular, directional waves past a semi-infinite breakwater. For irregular waves diffracting around the tip of a breakwater, there is a shift in the peak period of the spectrum. This is caused by the fact that different frequencies of the spectrum have different diffraction coefficients at a fixed place behind the breakwater. So, in contrast to regular waves, for irregular waves there will be a change in the peak period of the wave 55

56 spectrum. An example calculation from SPM (1984b) shows that the use of diffraction diagrams for regular waves in stead of the ones for irregular waves will underestimate the diffracted wave height at a certain point behind the breakwater (or the cape in this case). Refraction after Cape Kaliakra In the calculation of the diffraction around Cape Kaliakra, a constant water depth has been assumed between Cape Kaliakra and the project location. However, because in reality the depth decreases towards the coast, also refraction will take place. Hereafter, a short elaboration on the combined effect of diffraction around Cape Kaliakra and refraction between Cape Kaliakra and the project location will follow. Figure 3.22: Situation sketch of combined effect of diffraction around Cape Kaliakra combined with refraction. In Figure 3.22 a situation sketch has been given. The straight grey lines indicate the wave rays as they would occur, if only diffraction around Cape Kaliakra would occur. However, in reality, after the incoming wave rays have been bended around the cape, also refraction will play a role. An indication of the occurring pattern has been sketched with red lines. Due to only diffraction, waves that will be affected by a diffraction coefficient K of less then 0.06 will reach the project location. However, due to refraction, these wave rays will be bended off (see for example the red wave ray numbered 1) to a location east of the project location. Consequently, because of this effect of refraction, waves which have been affected by a higher diffraction coefficient K will reach the project location, for example red wave ray 3, which originates from the region of a K > However, due to the effect of refraction, wave heights will decrease again when the waves move towards the coastline. Summarizing: waves that reach the project location have a higher original K then 0.06, but due to refraction the height of the waves will be reduced again. Therefore, it will be assumed that the initial approach of only diffraction (described in the previous section) will give a representative indication of the reduction in wave height due to the combination of both diffraction around the cape and refraction. Conclusion The waves coming from the northeastern sector can t reach the project location directly, because of the sheltering effect of Cape Kaliakra. However, Cape Kaliakra will function as a diffraction point, causing waves from the northeast to bend around it. As has been mentioned earlier, all the incoming wave heights will be reduced by a factor equal to the diffraction coefficient K = In the table which can be found in Appendix C.2 (see column with heading near shore significant wave height ), the 56

57 results can be found. This table will give, together with the calculation results for the directions east, southeast and south (next section), the near shore wave statistics. It should be noted that for the near shore wave statistics for the direction northeast, the only thing that has been calculated is the significant wave height. That s why the cells of the other output columns for the direction northeast have been coloured grey SwanOne: shoaling, refraction, breaking, bottom friction (east, southeast and south) The computer program SwanOne will be used as a tool to calculate the transformation of waves from offshore towards the project location. SwanOne takes into account the effects of shoaling, refraction, breaking and bottom friction. The program can be used, because the assumption about parallel depth contours can be made. Wave rays from different directions will be investigated. These directions are east, southeast and south. SwanOne will not be used for the direction northeast, because Cape Kaliakra shelters the project location from waves from the northeast. First, the input for SwanOne will be described. Thereafter, the calculation of the near shore wave climate will be made. Bottom profile The bottom profile that will be used begins at a depth of 50 m. This has been done, because the available ARGOSS wave data have been obtained at a depth of 50 m, too. The bottom profile extends onshore until a depth of about 15 m, approximately 2500 m offshore of the location of the new artificial beach. At this point, the wave climate will be determined, in the form of a graph of exceedance probability of the significant wave height. The location of the bottom profile can be found in Figure The bottom profile has been made with the aid of the depth chart of THEMAP (2005). The bottom can be found in Figure As can be seen from Figure 3.24, the depth decreases while travelling onshore until approximately 17 m. Thereafter, there is a small increase in depth to approximately 20 m. Next, the profile continues until a depth of 15 m. The angle of the profile with respect to north is Figure 3.23: Location of bottom profile, indicated with black line (THEMAP, 2005). 57

58 Depth [m] Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Distance from offshore boundary [m] Figure 3.24: Bottom profile. Significant wave height H s and peak period T p For the directions east, southeast and south wave parameters for input in SwanOne, the table created in Appendix C.1 will be used. Each row of this table will be transformed to near shore wave conditions. SwanOne converts the input values for H s and T p to a H s and peak period T p to a Jonswap spectrum with a peak enhancement factor γ= 3 and a f -5 spectral tail (SWANONE USER MANUAL, 2009). Wave period From the ARGOSS database, values for the zero-crossing period T Z can be found. However, for the calculation of the near shore wave climate with the aid of SwanOne, the peak period T p is needed. If it is assumed that a wind sea spectrum will occur, the following conversion formula may be used (HOLTHUIJSEN, 2007): T T p (3.4) From this relation follows: T1 T 3 P (3.5) 0.95 Here it is assumed that the significant wave period T 1/3 is approximately equal to the zero-crossing period T z. Wind Regarding wind input, the scatter tables with information on the joint probability of occurrence of significant wave height and wind speed will be used. In the calculation, per occurring wave height class, one value of the wind speed will be taken. The wind speed with the highest probability of occurrence in a certain wave class will be taken. Water level As mentioned in Section 3.3, water level fluctuations will be neglected in this research. 58

59 Direction Direction [ ] Significant wave height Hs [m] Zero-crossing period Tz [s] Peak period Tp [s] Wind speed [m/s] Probability of occurrence [%] Probability of occurrence [-] Probability of non-exceedance P [-] Probability of exceedance Q [-] Number of storms per year (storm duration is 30 hours) Near shore significant wave height Hs,near [m] Relative peak period RTp [s] Mean wave period Tm01 [s] Mean zero-crossing period Tm02 [s] Mean energy wave period Tm-1,0 [s] Near shore direction [ ] Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Currents As mentioned in Section 3.4, currents in the Black Sea can be neglected. For this reason, no currents are entered as input in SwanOne. Other input settings Wave set-up will be taken into account during the calculations. Output In Appendix C.2, the result of the SWAN calculations can be found. In the table presented in Appendix C.2, several columns can be found. Furthermore, the same procedure as has been followed when making the offshore storm exceedance graph, has been followed to obtain the near shore exceedance graph. This has been done by sorting the near shore wave heights by increasing value. For the purpose of explanation, below, the header of the table has been displayed in Table 3.8. Table 3.8: Header of table with SWAN results. Offshore wave climate Probabilities Near shore wave climate Hereafter, the purpose of each column will be described: - Offshore wave climate: o Direction: The directional sector offshore, northeast, east, southeast or south. Source: ARGOSS database. o Direction. [ ]: Angle of wave incidence, corresponding to the above mentioned directional sectors. Northeast = 45 East = 90 Southeast = 135 South = 180 o H s [m]: Upper boundary of the significant wave height classes from the ARGOSS database scatter tables. o T z [s]: Upper boundary of the zero-crossing wave period classes from the ARGOSS database scatter tables o T p [s]: Corresponding peak period of T z, calculated with Equation (3.5). o Wind speed [m/s]: wind speed from the ARGOSS database, description see section Wind above. 59

60 - Probabilities: o Probability of occurrence [%]: Percentage of occurrence of a combination of the above mentioned H s and T p. o Probability of occurrence [-]: The same as the previous columns, but here it is a number instead of a percentage. o Probability of non-exceedance P: After sorting the data by increasing near shore wave height, this number indicates the probability of non-exeedance. o Probability of exceedance: The probability of exceedance, defined as 1 minus the above mentioned probability of exceedance. o Number of storms per year: see Section for an explanation on the calculation of the number in this column. - Near shore: o Near shore significant wave height H s,near [m]: Output value of the significant wave height H s, calculated with SwanOne (for direction east, southeast and south) or diffracted wave height (for direction northeast) o Relative peak period [s]: Output value of the relative peak period RT peak, calculated with SwanOne. o T m01 [s]: Mean absolute period, calculated with SwanOne. o T m02 [s]: Mean zero-crossing period, calculated with SwanOne. o T m-1,0 [s]: Output value of the Shallow water or mean energy wave period wave period, calculated with SwanOne. o Near shore direction [ ]: Mean near shore direction of wave propagation, calculated with SwanOne. In Figure 3.25 (next page) the results of the calculation can be found in graphical form. The probability of exceedance have been plotted against the occurring near shore wave heights. In Appendix C.2 the two columns that have been plotted are coloured yellow. For the same reason as with the offshore wave climate calculation, a trend line has been drawn by hand trough the data points. Conclusion From Figure 3.25 can be seen that the trend line tends to become horizontal on the right of the graph. If one looks at the last row of the table in Appendix C.2, it can be seen that this row, with a value of H s = 4.24 m has not been plotted as a point in the graph in Figure Because of the fact that the calculated number of storms per year with a H s = 4.24 m equals 0, the trend line will have an asymptote at H s = 4.24 m. 60

61 Figure 3.25: Probability of exceedance of significant wave height (near shore wave climate). 61

62 3.7 Sediment properties Regarding sediment properties, a distinction can be made between two types of sediment: the sediment that is present near the revetment (native material) where the new beach is going to be created and the material that will be used for to create the new beach (nourishment or borrow material) Sediment properties of sand near revetment The properties of the sediment that is present near the existing revetment have to be determined. These are important to determine the interaction between the existing sediment and the sediment that will be used to create the beach Sediment properties of sand used for nourishment The sediment that will be used for the creation of the new artificial beach, will be dredged from the sea bottom in the vicinity of the project location. The properties of this sediment have to be determined also, because they determine the stability conditions of the new beach. SAVOV (2005) describes a field investigation on the availability of suitable sand in the vicinity of the project location. By means of sand sampling and measuring the thickness of the sand layer on the bottom it became clear that plenty of sand is available at a distance of only 500 m from the project location. During the process of dredging the borrow material, the fine fraction of this material will be washed out. It will be assumed that the material from the clay and silt fraction, which is the material with grain diameters smaller than mm, will be washed out. Consequently, the material that will be used for dredging, will be courser than the original material and will have a higher mean grain diameter D Field research The locations of the samples that have been taken, can be found on the map displayed in Figure In the analysis of the results, a distinction will be made between the different areas: Four samples have been taken in the near shore area, which will represent the native material. From the shore in seaward direction, three samples have been taken in one cross-shore profile. These samples are numbered A3, A2 and 213. Another sample has been taken near the western groyne, which has the number C1. In the potential borrow area, 7 samples have been taken. These samples have been numbered 1, 5, 6, 9, 30, 32, and 160. One sample has been taken at a distance of approximately 800 m from the shoreline, to see whether this sand is suitable to use for dredging too. The number of this sample is 272. In Appendix D has been explained why these locations have been chosen. 62

63 Figure 3.26: The locations of the soil samples that have been taken Results of laboratory analysis The soil samples that have been obtained during the field research have been analysed in the Geotechnical Laboratory at the Faculty of Civil Engineering and Geosciences of Delft University of Technology. The sieve curves of the samples have been obtained by means of hydrometer tests. The method to be followed is described in a manual from Delft University of Technology written by MULDER AND VERWAAL (2006). By following this manual, the test will be carried out in accordance with the following standard: BS 1377: part 2: 1990 (BS stands for British Standard Institution). Also, the amount of calcium carbonate and the amount of organic materials of two samples have been investigated. These parameters are important, for amongst others the determination of the behaviour of the borrow material. Material containing a high percentage of light materials has a lower specific density, consequently this material will behave different then material with a higher specific density. In Appendix D a detailed description of the method used can be found. Also the results of the sediment analysis will be given in Appendix D. In this section a summary of the results will be given, concerning the sieve curves and connected to that the D 50 of the native and nourishment material. These are important parameters to determine the stability of the proposed beach. Density of grain material In order to obtain the sieve curves of the obtained samples, the density of the grain material has been obtained with the aid of an automatic gas pycnometer. More information on the use of an automatic gas pycnometer can be found in Appendix D. From 7 of the 12 samples that have been taken, the density has been determined. The mean of these values has been calculated. This mean value is kg/m 3. This value will be used as representative value to determine the sieve curves of all samples. This value may seem quite high, but the number can be explained by the high amount of calcium carbonate in the soil. 63

64 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Sieve curves near shore (native sand) In Figure 3.27 the sieve curves of the near shore samples have been displayed. From these graphs, an estimation for the mean grain diameter D 50 of the samples has been made. These estimated values can be found in Table 3.9. As can be seen, the value for D 50 of the three samples that have been taken in a cross-shore profile (A3, A2 and 213), is equal to approximately 0.1 mm. The sample that has been taken near the western groyne has a D 50 of approximately 0.18 mm, indicating that the material near the western groyne is somewhat coarser than the material halfway between the groynes. Hydrometer tests - Native material 100 A3 A2 213 C Grain size (mm) Figure 3.27: Sieve curves of the soil samples taken in the near shore area. Table 3.9: Estimations of several parameters of the samples taken in the near shore area. Sample number Estimation of D 50 [mm] Estimation of D 85 [mm] Estimation of D 15 [mm] D 85 /D 15 Percentage of fines [%] A A C In Table 3.9 the values of D 85 /D 15 of the sieve curves have been given. The value of D 85 /D 15 gives an indication of how uniform the grain material is distributed. The closer the value of D 85 /D 15 approaches 1, the more uniform the sample is distributed. As can be seen from the sieve curves of the samples itself, the middle part of the curves is quite steep, which indicates that the material is quite uniform distributed. This can also be seen from the values of D 85 /D 15, which vary between 2.6 and

65 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria In the last column of Table 3.9 the percentage of fines has been given per sample. The percentage of fines is the amount of material which has a grain diameter smaller than mm. This number is not important for the native material, but it is important for the nourishment material, because of the fact that it is assumed that during dredging the fine fraction will be washed out. As can be expected for near shore bottom material, because of action by breaking waves, the percentage of fines is not high, varying from 5.6 % (sample A3) near shore to 13.5 % (sample 213) 100 m from the shoreline. Sieve curves borrow area (original samples) In Figure 3.28 the sieve curves of the offshore samples have been displayed. From these graphs, an estimation for the mean grain diameter D 50 of the samples has been made. These estimated values can be found in Table As can be seen, the value for D 50 of most of the samples is approximately 0.1 mm, except for sample 1. Sample 1 is coarser than the other samples, with a value for D 50 of approximately 0.2 mm. Hydrometer tests - Borrow area Grain size (mm) Figure 3.28: Sieve curves of the soil samples taken in the borrow area. 65

66 Table 3.10: Estimations of several parameters of the samples taken in the borrow area. Sample number Estimation of D 50 [mm] Estimation of D 85 [mm] Estimation of D 15 [mm] D 85 /D 15 Percentage of fines [%] Average: 24.8 In Table 3.10 the values of D 85 /D 15 of the sieve curves have been given. As can be seen from the sieve curves of the sample itself, there is a large variation in steepness of the middle part of the sieve curves. This can also be seen from the values of D 85 /D 15. Sample 160 has the lowest value of D 85 /D 15, namely 1.8. Samples 6, 9, 30 and 32 have a slightly higher value than sample 160, varying from 4.0 to 8.5. Samples 1 and 5 have a high value of D 85 /D 15, which indicates that they have a very wide gradation. This can also be seen from the sieve curves itself. In the last column of Table 3.10 the percentage of fines has been given per sample. These values indicate how much material will be lost while dredging the material from the sea bottom. As can be seen from these values, the percentage of fines varies between 13.5% for near shore samples (sample 32) to 37.8 % for more offshore samples (sample 1). 66

67 Sieve curve far offshore point (original sample) In Figure 3.29 the sieve curve of the sample that has been taken far offshore (272) has been displayed. From this graph, an estimation for the mean grain diameter D 50 of the sample has been made. This estimated value can be found in Table The estimated value of D 50 for sample 272 is mm. Figure 3.29: Sieve curve of the soil sample taken far offshore (sample 272) Sample number Table 3.11: Estimations of several parameters of the sample taken far offshore. Estimation of D 50 [mm] Estimation of D 85 [mm] Estimation of D 15 [mm] D 85 /D 15 Percentage of fines [%] For the offshore sample that has been taken, the value of D 85 /D 15 has been determined. This value is 130, indicating that the sample has a quite wide graded distribution. The amount of fines is 62.9%, so the material is quite fine. 67

68 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Sieve curves course fractions of borrow material (larger than mm) The sieve curves of the samples of the fraction larger than mm have been displayed in Figure 3.30 and the corresponding mean grain diameters have been listed in Table Only this part of the soil will be left over during the dredging process. As can be seen, most of the samples have a coarse fraction with a mean grain diameter between 0.10 mm and 0.20 mm. The coarse fraction of sample 1 has a higher mean grain diameter, which amounts 0.46 mm. Sieve curves fraction > mm Grain size (mm) Figure 3.30: Sieve curves of the course part (larger then mm) of the soil samples taken in the borrow area. Table 3.12: Estimations of the D 50 of the course part (larger then mm) of the soil samples taken in the borrow area. Sample D 50 [mm] The more course fraction of samples 1 and 5 can be explained by the fact that a lot of larger grains are present in the samples. This can be seen on the pictures in Figure

69 Figure 3.31: Pictures of the course part (the part of the sample with grains larger than mm) of sample 1 (left) and sample 5 (right). 69

70 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Sieve curve course fraction of far offshore point (larger than mm) Just like with the borrow area material, in Figure 2.1 the sieve curve of the coarse fraction of the sample has been displayed. In Table 3.13 can be read that the mean grain diameter of this sample is 0.11 mm. Sieve curve fraction > mm Grain size (mm) Figure 3.32: Sieve curves of the course part (larger then mm) of the sample taken far offshore (sample 272). Table 3.13: Estimations of the D 50 of the course part (larger then mm) of the soil sample taken far offshore. Sample D 50 [mm] If one takes a close look at the sieve curve of the original sample 272, see Figure 3.29, it can be seen that the sieve curve consists of 3 parts. One part is the fine part smaller then mm, which will be lost if this sand will be used as nourishment material. The steep middle part has been labelled Coarse part 1, which is the part of the sand between mm and 0.15 mm. A third part is the less steep upper part, labelled Coarse part 2, with a diameter larger then 0.15 mm. The sieve curves of coarse part 1 and 2 have been plotted in Figure

71 Percentage passing (%) Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Coarse part 1: mm < Grain size < 0.15 mm Grain size (mm) Coarse part 2: Grain size > 0.15 mm Grain size (mm) Figure 3.33: Sieve curves of the course part 1 (larger then mm and smaller then 0.15 mm) of the sample taken far offshore (sample 272). From these sieve curves, the values for the mean grain diameter D 50 can be estimated for the two coarse parts. These values are listed in Table From Figure 3.29, an estimation of the percentage of the different fractions of the total have been made. These values have been summarized in the last column of Table Table 3.14: Data of coarse part 1 and 2. Sample Part D 50 [mm] Percentage of total sample [%] 272 Fine part n.a Coarse part Coarse part

72 Amount of calcium carbonate In this section the results of the determination of the amount of calcium carbonate will be presented. As mentioned before, the amount of calcium carbonate has been determined for two of the obtained samples. The goal of this test is to give a general indication of the amount of shell material that can be found in the area. This has been done by means of the titrimetric method by ROWELL (1994). This method has been described in Appendix D.4. Two samples have been analysed. The number of these samples are 5 and 32. In Appendix D.4, the results of the tests can be found. The general conclusion was: - The amount of calcium carbonate in sample 5 amounts 41%. - The amount of calcium carbonate in sample 32 amounts 52%. Sample 32 has been taken closer to the shoreline then sample 5. The above mentioned results indicate that closer to the shoreline the amount of calcium carbonate is slightly higher than further offshore. The values are rather high, from a first visual inspection could not be concluded that the amount of shell particles would be this high. The high amount of calcium carbonate can be explained by the fact that part of the bottom material consists of material eroded from the cliffs along the Bulgarian coast. These cliffs consist of limestone. This explains why the amount of calcium carbonate (lime) is high. So, it should be stressed that in this case the amount of calcium carbonate is not equal to the amount of shells. Amount of organic material When the dried samples are visually inspected, it can be seen that the amount of organic material is negligible in the samples. No more then a few percent of organic material is present in the samples Conclusions Grain diameter One conclusion that can be drawn from the results is that the average value of D 50 from both the native near shore material as the material from the potential borrow area is almost the same. This value is 0.1 mm. It could be expected that the near shore material would be somewhat coarser than the material further offshore, but this seems not to be the case. However, as can be seen from the sieve curves, the amount of fine material is higher for the borrow material than the native material. The value of D 50 of the far offshore sample equals mm. This indicates that the material offshore from the potential borrow area is finer than inside the borrow area. Course fraction of borrow material Next, the conclusions will be presented for both the borrow area and the more offshore material of the coarse part of the samples. - Borrow area: As mentioned above, the fine fraction of the borrow material (the part smaller than mm) will be washed out during the dredging process. Consequently, material with a higher mean grain diameter will remain which can be used for the creation of the beach. The mean grain diameter of the coarse fraction of the material in the borrow area has values between 0.10 and 0.20 mm. 72

73 - More offshore material: As stated before, the sieve curve of sample 272 could be divided into three parts, indicating that this sand in fact can be seen as a mixture of three different types of sand. From Table 3.14 can be concluded that about 60% of the sand will be lost during the dredging process, 30% of the material consists of sand with a mean grain diameter of 0.1 mm and 10% of the sand consists of a mean grain diameter of 1 mm. This indicates that if one is interested in making a stable beach with a relatively high mean grain diameter of 1 mm, this is possible with this sand. The sand can be divided into fractions by means of a device called a dredging hydro cyclone. This would mean that 90% of the material will be lost. If this is beneficial, will depend on a costs and benefits analysis. Percentage of fines The percentage of fines is the amount of material of the sample of which the grains are smaller than mm. This percentage will be lost during the dredging process. For the potential borrow area the percentage of fines varied from 13.5% to 37.8%. As can be seen in Table 3.10, the average percentage of fines amounts 24.8%. The percentage of fines in the offshore sample amounts 62.9%. The question whether this loss is acceptable is a matter of costs and benefits. Sediment transport calculations For the sediment transport calculations, representative values for the native material and the nourishment material have to be chosen. - For the native material, the value of 0.10 mm will be used as representative mean grain diameter. The samples which have been taken in a cross shore profile (A3, A2 and 213) all have a mean grain diameter which is approximately equal to this value. To check if the influence of the diameter of the grain material on the profile curve is large, also a calculation with 0.20 mm will be made, since the sample labelled C1 indicates that not everywhere the value of D 50 = 0.10 mm is representative. - For the borrow material, the diameter of the course part will be used, since only this part will remain after the dredging process. Most of the samples (coarse part) have a mean grain diameter between 0.10 mm and 0.20 mm. The coarse fraction of sample 1 has a higher mean grain diameter, which amounts 0.46 mm. Amount of calcium carbonate Two samples have been analysed to obtain an indication of the amount of shells (calcium carbonate) in the bottom material. It has been found that the bottom material consists for about 40% to 50% of calcium carbonate. On the first hand, the test to obtain the amount of calcium carbonate was intended to obtain an indication of the amount of shells. However, 40 to 50% of shells seems quite high for this bottom material. The high amount of calcium carbonate can be explained by the presence of eroded limestone material on the bottom. It is stressed again that in this case the determined percentages of calcium carbonate do not indicate the amount of shells. Organic material The amount of organic material in the samples is negligible. 73

74

75 Chapter 4 Required wave conditions The new artificial beach will be created with sand that will be dredged locally from the sea bottom. The purpose of the floating breakwater that has to be designed, is to make the beach profile dynamically stable. To achieve this dynamic stability, a certain maximum wave height is allowed behind the breakwater. This will be investigated by means of cross-shore sediment transport models. Also, a longshore transport model will be described in this chapter, because in longshore direction, the beach has to be stable also. First, a number of reference projects and previous investigations regarding the protection of sandy beaches by means of detached floating structures will be described in Section 4.1. When looking at these projects, insight will be gained regarding the performance of such structures and the beach response to the structure. Next, a description of several calculation methods on sediment transport will be given. Distinction will be made between longshore transport (Section 4.2 and 4.3) and cross-shore transport (Section and 4.4 and 4.5). At last, in Section 4.6, the conclusions of the investigations will be given. 4.1 Introduction Laboratory research on beach erosion control by a submerged floating breakwater In SHIMODA et al. (1991) a laboratory research on the use of a submerged floating breakwater to control beach erosion is described. The structure investigated is tension-moored, meaning that the mooring lines are tight, because of the fact that the structure is submerged. Beach profile types In their research, three beach profile types are distinguished. The beach type categorization has been adopted from SUNAMURA AND HORIKAWA (1974). In the laboratory tests the three beach types are produced by means of regular waves with different wave steepness. A beach has been set-up in a wave flume. The initial beach is plain with a slope of tan( ) 1/10. The beach material consists of fine sand with a median grain diameter D 50 = These beach types (see also Figure 4.1) are the equilibrium profiles at the end of the test, in the case no structure has been placed: - Eroded type beach, obtained with wave steepness H 0 /L 0 = Eroded type indicates that the shoreline has retreated and that only offshore sediment transport has taken place. - Intermediate type beach, obtained with wave steepness H 0 /L 0 = Intermediate type means that the shoreline has advanced and that both some onshore and offshore sediment transport has taken place. - Accreted type beach, obtained with wave steepness H 0 /L 0 = Accreted type indicates that the shoreline has advanced and only onshore sediment transport has taken place. 75

76 Figure 4.1: Three profile types (adapted from SUNAMURA AND HORIKAWA (1974)). Two-dimensional experiments After these tests, a model of the submerged tension-moored breakwater has been put into place in the wave flume. The flume used has dimensions of 1 m width, 1.5 m height and 50 m length. The floating breakwater model has dimensions height D = 10 cm, width B = 30 cm and length A = 99 cm. The distance between the shoreline and the breakwater is denoted with l x. the distance between the still water level and the top of the breakwater is denoted as d. The breakwater was fixed to the bottom with 4 stainless steel wires of 3 mm diameter. h is the water depth halfway the width B of the breakwater. The experimental set-up has been illustrated in Figure 4.2. Figure 4.2: Experimental set-up (SHIMODA et al., 1991). Several experiments were carried out, each time changing the submerged depth d of the breakwater or the distance to the shoreline l x. During the tests regular waves with several wave steepness were generated. The waves were generated for about 4 hours until the beach reached an equilibrium state. A dimensional analysis of the parameters involved, resolved that there are many leading factors involved with the equilibrium beach profile. Because the laboratory experiments are limited, the effect of l x /L and d/h have been mainly discussed in the paper. In general, the experiments showed that the bottom configuration change mainly took place in water depths shallower than the depth at the place of the breakwater. The change becomes smaller with increasing l x /L and decreasing d/h. 76

77 One experiment with wave steepness H 0 /L 0 = 0.06, without the breakwater in position, created an eroded-type beach. With the same wave conditions, but with the breakwater in place, the equilibrium beach profile changed to an uneroded-type or a little accreted type beach. The steep incoming waves were broken by the breakwater. The attenuated waves caused sediment to be transported onshore. However, in case the breakwater was placed on an intermediate type or accreted type beach, the bottom configuration was not significantly changed. In case the clearance between the bottom of the breakwater and the beach was less than the breaker height, the bottom around the breakwater was scoured. Sediment located onshore of the breakwater is suspended by the vortex induced by breaking waves over the breakwater. This sediment is transported away offshore. The maximum observed dimensionless scour depth hh0 is less than h is defined as the maximum vertical distance between the original bottom and the eroded profile. Three-dimensional experiments In a wave basin with a width of 10 m, a height of 0.65 m and a length of 30 m, 3-dimensional tests with submerged tension-moored breakwaters have been carried out. These tests were performed to investigate the combined influence of transmitted and diffracted waves on the beach response. Three breakwater dimensions have been tested which are listed in Table 4.1. Table 4.1: Different breakwater dimensions Breakwater Height D [cm] Width B [cm] Length A [cm] The breakwater models were attached to the bottom with steel wires of 0.3 cm diameter. Furthermore, the beach material and initial bottom configuration were quite the same as during the two-dimensional experiments. Several regular wave climates have been applied. The waves were generated for about 6-12 hours, until the beach reached an equilibrium state. Because of the fact that the number of laboratory tests is limited, only the effect of D/h, d/h, l x /L, A/l x and K/A were treated in the paper. Several positions with respect to the coast in case of one breakwater have been tested. These tests revealed that in case the breakwater is placed at an accreted-type or a intermediate-type beach, accretion will take place in the form of a spit. Depending on the breakwater dimensions and the distance between the shoreline and the breakwater, a single-peaked, double-peaked or triple-peaked spit will develop. In case of an eroded-type beach, no spit was formed. The erosion of the beach was stopped and the shoreline was restored to its original position. Also cases with two breakwaters with a certain gap with between them have been tested. It was observed that in case of an accreted-type beach or an intermediate-type beach, spits were formed behind the breakwaters. In the case of two breakwaters being placed in front of an eroded-type beach, the shoreline erosion stops. Conclusion The main conclusion that was drawn from the research was that on all the three type of beaches (eroded, intermediate and accreted), the submerged tension-moored breakwater served as a good measure to control beach erosion. It was mentioned that it is possibly a good measure against beach erosion in an area where huge waves will not occur. 77

78 4.1.2 Prototype experiments on floating structures in Lake Grevelingen, The Netherlands In the Dutch province of Zeeland, many estuaries can be found. After the creation of the Delta Works, hydraulic boundary conditions regarding tidal flow and wave action have been changed in these estuaries. These changes have consequences for the morphology of the estuaries. In many cases the changes induced unwanted erosion. To counteract this erosion, special measures had to be taken. To investigate the possible use of floating structures to counteract the erosion, a field experiment has been conducted in Lake Grevelingen. This experiment has been described by PILARCZYK et al. (1986a). Two types of structures were placed in position on the sandy shore of the island Veermanplaat in Lake Grevelingen, namely: - Units of four plastic pipes of 0.7 m diameter and 10 m length, each connected together flexible. - Seven wooden floating drafts of dimensions 5.2 x 3.3 x 0.3 m. These were connected together using nylon rope and chains. The total length of each experimental section was approximately 200 m and the distance between the structures and the shoreline is about 300 m. The local water depth varies between 1.0 and 1.2 m. Transmission coefficients have been measured and showed values between 0.55 and 0.8. The wave attenuation however is not sufficient, erosion still takes place. Possible reasons that the erosion still takes place could be that the local wave growth between the breakwater and the shoreline is underestimated, possible longshore transport due to wave attack under an angle or limited length of the construction, allowing wave penetration at both sides of the construction. 4.2 Longshore sediment transport, theoretical background In this section, calculation methods to determine longshore sediment transport will be described CERC formula The CERC formula has been developed by the Coastal Engineering Research Center (CERC) of the American Society of Civil Engineers. The formula has been developed in the 1940 s. This was long before the longshore current theory was developed. The formula has been calibrated with many laboratory and prototype measurements. The formula gives the bulk longshore sediment transport, induced by wave action approaching the coast under an angle (BOSBOOM AND STIVE, 2010). The CERC formula can appear in many forms. In BOSBOOM AND STIVE (2010) the following notation of the CERC formula can be found: K S s p g sin H b s, b (4.1) Where: S = deposited volume of sediment transported (including pores) [m 3 /s] K = constant [-] ρ = density of the water [kg/m 3 ] s = relative sediment density ρ s /ρ [-] ρ s = density of the grain material [kg/m 3 ] p = porosity of transported material [-] g = gravitational acceleration [m/s 2 ] 78

79 γ = breaking parameter [-] φ b = wave angle of incidence at breaking point [ ] H s,b = significant wave height at breaking point [m] The constant K has a value of With the aid of this formula, the longshore sediment transport due to several wave heights and angles can be computed Formula of Kamphuis The above mentioned CERC formula does not take into account the grain size of the beach material and the beach slope. BOSBOOM AND STIVE (2010) mention an empirical relationship developed by Kamphuis in The relationship is a bulk longshore transport formulation, based on an analysis of field and laboratory data. The following relationship was suggested: I 2.27H T m D sin s, b p b b (4.2) Where: I = the amount of transported sediment [kg/s] H s,b = significant wave height at breaking point [m] T p = peak period at the breaking point [kg/m 3 ] m b = tan α b = beach slope at the breaking point [-] D = grain diameter [m] φ b = wave angle of incidence at breaking point [ ] To calculate the transport in volume per time unit S, the following formula can be used: S 1 p s I (4.3) Where: S = deposited volume of sediment transported (including pores) [m 3 /s] I = the underwater weight of sediment transported [kg/s] ρ s = density of the grain material [kg/m 3 ] ρ = density of sea water [kg/m 3 ] p = porosity of transported material [-] Choice of longshore transport formula In this section, a choice will be made on which of the two above mentioned longshore transport formulae to use for longshore transport calculations. The two above mentioned formulae are empirical relations that are based on laboratory and field data. The formula of Kamphuis includes more parameters than the CERC-formula, namely the grain size and the beach slope. That s why the formula of Kamphuis will be used for the calculation of the longshore sediment transport. 79

80 4.3 Longshore sediment transport, application of theory Longshore sediment transport formula by Kamphuis As mentioned in Section 4.2.3, the formula for longshore sediment transport by Kamphuis will be used. The modelled situation has been sketched in Figure 4.3. The real coastline of the project location is not straight. However, for the calculation of the longshore sediment transport rates, it is assumed that the coastline can be modelled as a straight line. The straight schematized coastline that will be used has been displayed in Figure 4.3. Figure 4.3: Straight schematized coastline and calculation of angle of incident φ Input wave climate As can be seen from the formula of Kamphuis, the significant wave height, peak period and angle of incidence of the incoming waves at the point of breaking are necessary. The wave climate at a depth of 15 m has been determined in Section However, this is not the breaking point for the incoming waves, the wave transformation from the depth of 15 m to the breaking point has to be calculated first. This will be done by means of a calculation of the occurring shoaling, refraction and breaking between the point of 15 m and the point of breaking. The calculation results can be found in a table in Appendix F. Each row of the wave climate table determined in Section will be transformed. To do so, the earlier mentioned programme CRESS (2010) could be used. The programme SwanOne could also be used to calculate the breaker parameters. It has been chosen to use the programme CRESS, because this programme calculates the breaker parameters directly. CRESS has a pre-programmed routine which calculates the wave transformation due to shoaling, refraction and breaking from deep water to the point of breaking, under the assumption that the depth contours are parallel. CRESS calculates the breaking wave parameters by means of an iteration procedure that will be elaborated later. This means that, in order to use CRESS to calculate the wave climate at the breaking depth, a trick has to be applied to calculate a fictitious wave climate at infinite distance from the 15 m depth contour. This trick and the remainder of the calculation method will be explained hereafter. 80

81 Figure 4.4: Calculation of input climate for longshore sediment transport calculation. Table 4.2: Header of longshore sediment transport calculation table from Appendix F. For the purpose of explanation, the columns have been numbered. 81

82 In Figure 4.4 the method is explained. In Table 4.2 the header of the calculation table has been displayed for the purpose of explanation of the calculation procedure. The columns have been numbered for the purpose of explanation. The trick involves the backwards calculation of the wave climate from a depth of 15 m to a fictitious wave climate at infinite distance from the shoreline. Next, with the data fictitious point, the wave data at the point of breaking can be calculated. Before the calculation can be started, the incoming wave angle relative to north (from the climate at 15 m depth) has to be transformed to the angle of incidence relative to the normal of the straight schematized coastline. This procedure can be seen infigure 4.3. The angle relative to north of the normal to the schematised coastline is called α. Since the straight schematized coastline has been drawn more or less arbitrary, the real value for α is difficult to estimate. In the following calculations, a value of α = 16 has been chosen. This value will result in an indication of the occurring longshore transport. However, it should be kept in mind that the value of α might be 2 degrees more or 2 degrees less. It is expected that this difference won t result in significant differences regarding the final result of the longshore transport calculation. A random wave with a certain angle relative to north has been indicated. The angle between the direction of wave propagation and the normal to the schematized coastline is called φ. As can be seen from Figure 4.3, the angle φ can be calculated as follows: 180 Angle with respect to North (4.4) The angle of incidence with respect to north at a depth of 15 m can be seen in column 5. The corresponding angle φ will be calculated in column 6. The parameters that are known are the wave parameters at a depth of 15 m: - Significant wave height H s15 (column 3) - Peak period T p15 (column 4) - Angle of incidence φ 15 (column 6) The value of the peak period at 15 m depth T p15 will also be used as infinite wave period T p. Just for the overview, the values for T p have been displayed in column 13. Because of this fact, from now on T p will be called T p15. Next, the fictitious wave length at infinity corresponding to the peak period L will be calculated in column 14, by means of the following formula CRESS (2010): L g T 2 p15 (4.5) Where: L = deep water wave length corresponding to T p [m] g = gravitational acceleration [m/s 2 ] T p15 = wave length at a depth of 15 m [m] Next, in columns 7 and 8, the wave length at a depth of 15 m can be calculated. This will be done by means of the approximation by Visser, which is described in the help file of CRESS (2010): 82

83 h 15 h15 L15 gh15 1 Tp15 for 0.36 L L h L15 L L 15 for 0.36 (4.6) Where: L 15 = wave length at a depth of 15 m [m] The cell in column 8 will be coloured green if the upper row of equation (4.6) has to be applied, otherwise it will remain white. The change in direction of wave propagation between two random points above a bottom with parallel depth contours can be calculated by means of the following formula (CRESS, 2010): L arcsin sin L (4.7) Where: φ 15 = angle of wave incidence at a depth of 15 m [ ] φ = (fictitious) deep water angle of wave incidence [ ] However, the angle of wave incidence at the fictitious infinite point has to be calculated. To do this, equation (4.7) can be rewritten to equation (4.8). The results calculated by this equation are listed in column 14. L arcsin sin 15 L15 (4.8) Now, all the above determined data can be used to calculate the refraction coefficient K s15 and shoaling coefficient K s15 to transform the wave height from a depth of 15 m to the fictitious point at infinite distance from the shoreline. The diffraction coefficient is calculated by equation (4.9) and the results are listed in column 9. K r 15 cos cos 15 (4.9) The shoaling coefficient is calculated by equation (4.10) and the results are listed in column 10. K s h 15 2 h15 tanh 1 L15 2 h 15 L15 sinh L 15 (4.10) 83

84 Where: h 15 = water depth = 15 m As a last step to obtain the wave climate at the fictitious point at infinite distance, the fictitious significant wave height H s can be calculated as follows: H s H K K s15 (4.11) r15 s15 Now, in columns 11, 12, and 13, an input wave climate for the calculation from the fictitious point to the breaking point has been obtained. In fact, the following expression will be applied to calculate the significant wave height at breaking depth: K K H H K K r, br s, br s, br s15 (4.12) r15 s15 In this expression, the refraction and shoaling coefficient at breaking depth K r,br and K s,br will be calculated by means of an iteration procedure by the program CRESS. In Appendix G, the calculation and iteration procedure used by CRESS has been explained. The output of the CRESS iteration can be found in columns 15, 16, 17, 19 and 20 (in column 18 the peak period at a point of 15 m has been repeated for completeness, this is no output value of CRESS). In fact, the entire procedure as described above will be followed, additionally the point of breaking will be determined by means of an iteration. Because of the fact that random waves are being calculated, a value for the breaker parameter of γ br = 0.5 will be assumed. CRESS output: - Refraction coefficient at breaking depth K r,br (column 15) - Shoaling coefficient at breaking depth K s,br (column 16) - Significant wave height at the breaking point H s,br (column 17) - Peak period at breaking point T p,br (this is period is assumed to be equal to the peak period at a depth of 15 m, this is no output value of CRESS) (column 18) - Angle of wave incidence at the breaking point φ br (column 19) - Breaker depth h br (column 20) 84

85 4.3.3 Longshore sediment transport calculation for current situation Next, the formula for longshore sediment transport by Kamphuis will be used to calculate the contribution to the total yearly transport of each row of the wave climate table. This calculation will be executed for the current situation, so with the native sand. The formula reads (repeated): I 2.27H T m D sin s, b p b b (4.13) Where: I = the amount of transported sediment [kg/s] H s,b = significant wave height at breaking point [m] T p = peak period at the breaking point [kg/m 3 ] m b = tan α b = beach slope at the breaking point [-] D = grain diameter [m] φ b = wave angle of incidence at breaking point [ ] The following data are needed to use the formula of Kamphuis: - The wave parameters at the breaking point H s,b,, T p,b and φ b. - The bottom slope m b can be estimated from the cross shore profiles displayed in - Figure 4.8. The value for the bottom slope has been estimated to be m b = The value for the grain diameter D will be taken equal to the mean grain diameter D 50 as has been obtained from the sieve curves in Section The value of D 50 for the native material that has been obtained was 0.1 mm = m The results of this calculation are listed in column 21. Now, the mass of the transported sediment is known as a mass transport per time unit I. Next, this quantity will be converted to an equivalent volume transport per unit of time unit S by using equation (4.3), which reads (repeated): S 1 p s I (4.14) Where: S = deposited volume of sediment transported (including pores) [m 3 /s] I = the underwater weight of sediment transported [kg/s] ρ s = density of the grain material [kg/m 3 ] ρ = density of sea water [kg/m 3 ] p = porosity of transported material [-] These are the input values that are needed for the use of equation (4.14): - The density of the grain material ρ s has been determined in Section The value obtained was kg/m 3. The density of sea water will be estimated to be 1025 kg/m 3. - The porosity p will be assumed to be equal to 0.4. The results of the use of equation (4.14) are displayed in column

86 Now, the volumes per year have to be calculated. This will be done by multiplying the values from column 22 by the number of seconds in a year. Next, the number will be multiplied by the probability of occurrence of a certain wave height which are listed in column 2. The final results per occurring wave height are listed in column 23. Positive transport values are directed westward and negative transport values are directed eastward Results: yearly longshore sediment transport quantities The net total yearly longshore transport rates and the results per direction (westward and eastward) can be found in the table in Appendix F. They can also be found in Table 4.3. Table 4.3: Longshore sediment transport results. A positive number means transport is in westward direction, negative means in eastward direction. Quantity Transported volume S [m 3 /year] Total net transported volume Transport in westward direction Transport in eastward direction Remarks The following remarks have to be made regarding the calculation of the longshore sediment transport: - It will be assumed that at every point in a cross shore profile, the peak period doesn t change. This means that at every point, the peak period has the value of the peak period at a depth of 15 m T p15. - For the waves at a depth of 15 m that have been calculated by means of diffraction around Cape Kaliakra (which originate offshore from the north-eastern direction), no angle of wave propagation at a depth of 15 m has been calculated. Because of the effect of diffraction around Cape Kaliakra (see Figure 3.21), a direction of 110 with respect to north will be assumed. - For these waves, also no peak period has been calculated. It is assumed that the original offshore peak periods equal those at a depth of 15 m. - In column 14 of the calculation, equation (4.8) is used to calculate the fictitious wave angle φ. To do so, an expression containing an arcsine has to be solved. The value of this arcsine can t be larger then 1. However, in five of the rows in the longshore transport calculation table, this is the case. To overcome this problem, the relative peak period at 15 m T p15 has been lowered to a value where the problem didn t occur. In column 4, the 5 cells involving this problem have been coloured red. - It can be expected that the value of the shoaling coefficient at the breaker depth K s,br doesn t differ much from the shoaling coefficient at a depth of 15 m K s15. This is the case for the waves which originate from offshore directions east, southeast and south. However, for the direction northeast, the values of K s,br are significantly higher then K s15. This can be explained by the fact that these waves are relatively long, with a low wave steepness. This kind of waves undergo a lot of shoaling while propagating towards the coastline Sea breeze effect A phenomenon that has not been taken into account while determining the longshore transport rate, was the effect a sea breeze might have. On relative calm days, the wave climate is influenced by waves generated by sea breeze. These see breeze waves might have a significant effect on the longshore transport rate. The sea breeze is generated by a temperature difference between land and 86

87 sea. For more information on this phenomenon is referred to a paper by VERHAGEN AND SAVOV (2006). For the calculation of the longshore transport rates, only the offshore wave data from the ARGOSS (2010) database have been used Blocking effect of groynes Approach As has been described in Chapter 2, the project location is situated between two existing groynes. Because of these groynes, part of the generated longshore transport will be blocked. In this section will be calculated which part of the longshore sediment transport is not blocked by the groynes. To do so, it is assumed that the cross-shore velocity distribution can be schematised as a triangle with its minimum at the coastline and the maximum at the breaker line. The longshore current generated by breaking waves in the surf zone is responsible for the longshore transport of the sediment, the orbital velocity under the waves stir the sediment in suspension. Because of the fact that the longshore velocity has a low value in comparison to the orbital velocities near the bottom, it can be assumed that the cross-shore distribution of the longshore sediment transport may be schematized as a triangular shape too, see Figure 4.5. In this distribution, the area of the total triangle is the yearly longshore sediment transport flux which was calculated in Section The calculation has been executed per row of the longshore sediment transport calculation table, see Appendix F. The table has been extended by 5 columns, in which the results of the calculation can be seen. The header of this part of the table can be seen in Table 4.4. Figure 4.5: Calculation of the blocking effect of the groynes 87

88 I [kg/s] S [m 3 /s] Transported volume S [m 3 /year] Positive = westward Negative = eastward Distance from coastline where wave breaks Lbr [m] s max [m 3 /year/m'] s gr [m 3 /year/m'] S blocked [m 3 /year] S passed [m 3 /year] Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Table 4.4: Header of calculation of blocking effect by groynes. Longshore transport Blocking effect of groynes During the iteration process of determining the breaking wave height, the breaker depth h br has been calculated, too. With the breaker depth known, the distance from the shoreline to the breaking point (which is equal to the width of the surf zone) can be read from the bathymetry maps in Figure 3.4 and Figure 3.5. This distances have been listed in column 24, the symbol representing this distance is L br, see Figure 4.5. L gr represents the length of the groynes. The groynes are 120 m long. If the value of L br of a certain incoming wave is smaller then the length of the groynes L gr, the total longshore transport generated by that wave is being blocked by the groyne. In column 24 is checked whether this is the case or not. If L br is smaller then L gr, the cell will be coloured green. If this is not the case, the volume of sediment passing the tips of the groynes will be calculated as follows: The total transported amount of sediment S total is equal to the surface of the triangle. This area can be calculated by (see Figure 4.5.): S total L s (4.15) 1 2 br max This expression can be rewritten to Equation (4.16), from which the maximum value of the longshore transport at the breaking point s max can be calculated. This value has the unit of volume per time unit per unit of cross-shore distance (m 3 /year/m 1 ). For the results of this step, see column 25 of the longshore transport calculation table. s S total max (4.16) 1 2 Lbr Next, the value of longshore transport at the tip of the groyne s gr can be calculated by (see column 26): s L gr gr smax (4.17) Lbr 88

89 Consequently, the blocked yearly volume can be calculated by (column 27): S L s (4.18) 1 blocked 2 gr gr Now the yearly volume that has bypassed the tip of the groynes S passed can be calculated by subtracting the blocked yearly volume S blocked from the total yearly volume S total (column 28): S passed Stotal Sblocked (4.19) At last, all the values in the column of S passed can be added to get the total yearly volume of sand that leaves the project area due to longshore sediment transport Conclusion In Table 4.5, the results of the above calculated passed volumes have been summarized. Quantity Table 4.5: Summary of longshore transport calculations. Total transport [m 3 /year] Volume passed groynes [m 3 /year] Percentage of total that bypassed groynes [%] Total volume bypassed Transport in westward direction Transport in eastward direction In total 5308 m 3 of sediment leaves the project area because of longshore sediment bypassing the groynes. From this total amount 4735 m 3 is transported across the western groyne in western direction. This is approximately 39% of the total yearly westward transported volume. From the total amount -600 m 3 across the eastern groyne in eastern direction. This is approximately 39% of the total yearly eastward transported volume. 4.4 Cross-shore sediment transport, theoretical background In this section, calculation methods to determine cross-shore sediment transport and profile changes will be described. In literature, models describing these sediment transports can be found Bruun In 1954, Bruun analyzed a data set of beach profiles form the Danish North Sea Coast and Mission Bay in California, USA (DEAN, 1991). It was found that the beach profiles followed this simple power law: h( y) 2 Ay 3 (4.20) Where: h(y) = water depth at a distance y from the shoreline [m] A = scale parameter [m 1/3 ] y = distance from the shoreline [m] 89

90 4.4.2 Dean In 1977 Dean (DEAN, 1991) analyzed a data set existing of 504 beach profiles along the Atlantic Ocean and Gulf of Mexico coasts of the USA. A least squares method was used to fit a relation of the following form to the data: h( y) n Ay (4.21) A central value of n 2 3 was found, as Bruun found earlier in Dean showed that Equation (4.20) is consistent with uniform wave energy dissipation (loss in wave power) ε per unit volume of water across the surf zone, for a certain grain size. The wave energy dissipation ε can be expressed as: 1 EC G (4.22) h y Where: ε = wave energy dissipation per unit volume [W/m 3 ] h = water depth [m] y = distance from the shoreline [m] E = wave energy density [J/m 2 ] C G = group velocity of the waves [m/s] The shape parameter A can be expressed with the following expression: 2 3 D 24 A g (4.23) Where: A = scale parameter [m 1/3 ] ε = wave energy dissipation per unit volume [W/m 3 ] D = grain diameter [m] ρ = water mass density [kg/m 3 ] g = gravitational acceleration [m/s 2 ] γ = breaker parameter [-], expressed as: H (4.24) h Where: H = wave height [m] h = water depth [m] A sediment particle with a given diameter D has a certain stability while lying on the sea bed. Wave breaking induces regular wave motion to be transformed into turbulent wave motion. These turbulent motions cause destructive forces on the sea bed. If these forces are too great, movement of the sediment particle is induced. Particles are moved offshore, causing a gentler beach profile to develop. This milder slope reduces the wave energy dissipation per unit volume, which eventually leads to an 90

91 equilibrium profile. This is why the shape parameter A is a function of the sediment particle diameter D, via the wave energy dissipation ε. Dean showed in 1987 (DEAN, 1991) that the scale parameter A can be expressed in terms of the fall velocity of the sediment particles, by the following equation: A w (4.25) Where: A = scale parameter [m 1/3 ] w = fall velocity [cm/s] In Table 4.6 a summary of recommended values for the shape parameter can be found, in relation to their corresponding grain diameter. Table 4.6: Summary of recommended A-values in m 1/3. To find the corresponding value of A to a certain grain diameter D (in mm), one has to look up the first decimal of D in the most left column and the second decimal in the upper row. The corresponding A-value can be found at the intersection of the corresponding row and column (DEAN, 2002). With the equations mentioned above, a relation has been found between a certain grain diameter and the description of the corresponding equilibrium beach profile. However, also a certain relation with the occurring wave height has to be found, in order to determine what maximum wave height is allowed for a stable beach Closure depth A parameter that is related to the occurring wave height near the beach profile, is the so-called closure depth. The closure depth is the depth at the seaward limit of the effective seasonal profile fluctuations (DEAN, 2002). The closure depth is an important engineering concept, because it gives an indication of the seaward limit of the volume of sand to be nourished. In DEAN (2002) is mentioned that Hallermeier (in 1978 and 1981) developed the first rational method to calculate the closure depth. Hallermeier reasoned that the closure depth would be related to wave heights that would only rarely occur. It was decided to use the effective significant wave height, H e, which is the wave height that is exceeded only 12 hours per year, or 0.14% of the time. Hallermeier determined that the approximate closure depth h * could be expressed as 91

92 2 H e h* 2.28He gte (4.26) Where: H e = effective significant wave height [m] T e = wave period associated with H e [s] H e can be approximated from the annual mean significant wave height, H, and the standard deviation of the wave height, σ H, with: H H 5.6 (4.27) e e In 1985 Birkemeier used higher quality field measurements to evaluate Hallermeier s expression. Slightly different constants were recommended in the equation proposed by Hallermeier: 2 H e h* 1.75He gte (4.28) Hallermeier also found that the next simplified equation provided a good fit to the data, too: h* 1.57H e (4.29) DEAN (2002) further mentions that it should be kept in mind that h * is related to wave heights that are exceeded only 12 hours per year. Therefore it is likely that the closure depth would change from year to year. Another point that should be kept in mind is that in beach nourishment projects, the initial slope could be quite steep. That s why transport of sediment to greater depths than the closure depth can occur, due to bigger influence of gravity Vellinga Another method to describe a profile can be found in BOSBOOM AND STIVE (2010). This method is the method of equilibrium profiles by Vellinga. Instead of looking at the long term wave regime, this method describes the erosion profile of a beach that will develop during a storm. Vellinga developed a scale relation showing the effect of the grain size on a erosion profile shape. From this scale relation an equilibrium profile shape can be derived: h Ax' 0.78 (4.30) Where: x = horizontal distance from waterline A = non-dimensionless shape factor [m 1/3 ] The shape factor has also been derived from the scale relation developed by Vellinga: A w (4.31) 92

93 Where: w = fall velocity of grains [m/s] Beach nourishment When a beach will be nourished, the sediment size of the nourished sand can be the same as the native sand or may differ from that of the native sand. Nourished sand same size as native sand DEAN (2002) mentions that if the nourished sand is compatible in size with the native sand, the entire profile will move seaward over a certain distance Δy 0. It can be calculated with the following equation: y 0 V h B * (4.32) Where: V = nourished sand volume per unit coastline length [m 3 ] h * = closure depth [m] B = berm height [m], this is the height of the berm above sea level Nourished sand different size as native sand Often the sand that will be used for the beach nourishment will not be the same as the native sand. Consequently, if the borrow sand is coarser then the native sand, a steeper profile then the native profile will develop. If the borrow sand is finer then the native sand, a gentler profile will develop. In VERHAGEN (1996) a method has been described to get an estimation of how the new profile will look like. It is recommended to use the existing profile as starting point and to use scale relations to calculate the changes in beach slope. The scale relation to be used has been adopted from a paper by PILARCZYK et al. (1986b). The relation reads: l l w w (4.33) Where: l 1 = a characteristic (horizontal measured) length in the original profile [m] l 2 = a characteristic (horizontal measured) length in the nourished profile [m] w 1 = fall-velocity of the native material [m/s] w 2 = fall-velocity of the nourishment material [m/s] For the calculation of the fall velocity, the earlier mentioned computer program CRESS (2010) will be used. CRESS calculates the fall-velocity by the following formula: W W gd for D m gD 1 for m m D 2 50 D 50 W gd D for m (4.34) 93

94 Where: Δ = relative density [-] D 50 = mean grain diameter [m] ν = kinematic viscosity of water [m 2 /s] g = gravitational acceleration [m/s 2 ] More information on the use of formula (4.34) can be found in Appendix E. In this appendix, the formulae can be found to calculate the relative density (which depends on the salinity and the temperature of the water) and the kinematic viscosity (which depends on the temperature of the water). In SHUISKY (1993) information regarding the salinity and temperature of the water of the Black Sea can be found. Representative values were found to be a temperature of 15 C and a salinity of 16. With the aid of another routine from CRESS (2010), the density of the sea water can be calculated. With the afore mentioned values for temperature and salinity, the sea water density was found to be ρ w = 1011 kg/m 3. From the relation (4.33) becomes clear that if the borrow sand is coarser then the native sand, a steeper profile then the native profile will develop. If the borrow sand is finer then the native sand, a gentler profile will develop. This has been illustrated in Figure 4.6. From this figure can be concluded that the use of nourishment material which is coarser than the native material (w 2 < w 1 ) is profitable in view of the amount of material that is needed to achieve a certain beach widening (PILARCZYK et al., 1986b). Figure 4.6: Effect of grain size in steepness of nourished profile (VERHAGEN, 1996). 94

95 4.5 Cross-shore sediment transport, application of theory In this section, the above described calculation methods will be used to determine the required wave conditions for a dynamically stable beach Current situation In this section, the cross-shore profile of the current situation will be investigated. To do this, three beach profiles have been taken from the in situ measured bathymetry. The locations of these profiles have been indicated in Figure 4.7. The cross-shore profiles have been displayed in Figure 4.8. Figure 4.7: Location of the cross-shore profiles. 95

96 Depth [m] Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Distance from shore [m] Profile 1 Profile 2 Profile 3 Revetment 1 Revetment 2 Revetment 3 Figure 4.8: Cross-shore profiles. The presence of the revetment has been indicated with a vertical line on each profile. The profiles have been shifted horizontally with respect to each other, in order to let the lower part of the profiles coincide as good as possible. As can be seen, profile 1 has the shape of an erosion profile. The other two profiles follow more or less the same line. Equilibrium Dean profile Next, the cross-shore profiles will be compared to an equilibrium profile according to the equation of Dean (equation (4.21)). Only the lower part of the profiles will be taken into account in this comparison. The upper part of the profile will be disregarded, as this part of the profile will be influenced by the presence of the revetment. In Figure 4.9 the Dean profile corresponding to the native material has been displayed with a grey dotted line. The curve is based on the value of D 50 = 0.1 mm for the native material that has been obtained in Section The curve has been shifted 120 m to the left, in order to try to let the Dean curve to coincide as good as possible with the lower part of the cross-shore profiles. To know until what depth the Dean curve is valid, the closure depth H * (see Section 4.4.3) belonging to the governing wave climate has to be calculated. 96

97 Depth [m] Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Distance from shore [m] Closure depth -6 Profile 1 Profile 2 Profile 3 Dean profile (D50 = 0.1 mm) Closure depth Revetment 1 Revetment 2 Revetment 3 Figure 4.9: Three cross-shore profiles and the Dean profile for the native material with a mean grain diameter D50 equal to 0.1 mm. Closure depth As has been mentioned in Section 4.4.3, for the calculation of the closure depth, the so-called effective wave height H e is needed. This is the wave height that is exceeded only 12 hours per year, or 0.14% of the time. To obtain this value from the wave statistics that have been determined at a depth of 15 m, in Figure 4.10 the probability of exceedance values of a certain significant wave height H s have been plotted. The source of the data is the table with near shore wave statistics which can be found in Appendix C.2. In fact, it is the same graph as the storm exceedance graph which has been determined in Section 3.6.5, but the graph has been shifted horizontally. From this graph, the wave height that is exceeded for 0.14 % of the time can be estimated. From Figure 4.10 can be seen that the value of the effective wave height H e can be estimated to be equal to 3.75 m. This value occurs at a depth of 15 m. However, the near shore value of H e is necessary to calculate the closure depth of the native profile. 97

98 Figure 4.10: Determination of effective wave height H e at a depth of 15 m, which is needed to calculate the closure depth. The breaker wave height will be used as representative near shore wave height. To convert the value of H e at 15 m to the corresponding value at the breaking point, the same trick as applied in Section will be used. As a result, a breaking wave height (which will be used as effective wave height) of 3.98 m has been obtained. A corresponding value for T p = 8.96 s will be used. Now the value for h * can be calculated by Equation (4.28): 2 2 H 3.98 e h* 1.75He m 2 2 gte e (4.35) The closure depth has been indicated with a line in Figure 4.9. As can be seen, the line of the closure depth does not intersect the cross-shore profiles and the Dean curve within the image. This indicates that the plotted equilibrium Dean profile is not a good model for the real cross-shore profiles. Conclusion The formula of Dean is not a good representation of the actual bottom profiles. The conclusion that can be drawn from this is that the current profiles are not in equilibrium, according to Dean s theory. It can be expected that seaward directed sediment transport will occur, in order to reach the equilibrium Dean profile. Also, in this situation it is not possible to develop a complete Dean profile, because of the presence of the revetment and the rock layer under the sediment layer. As described in Section 4.4.5, when a beach nourishment takes place on a coast that has a stable profile (which for example can be a Dean shaped profile) a scale law can be applied in order to obtain the shape of the nourished profile. In this case the native profile appears not to be stable, because the equilibrium profile belonging to the grain size of the native material do not coincide. That s why in this case the scale law can not be applied to obtain the new profile. 98

99 Depth [m] Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria New situation The new artificial beach will be made with sand dredged from the local sea bottom. In this section, calculations regarding the interaction between the native material and the to be nourished material will be made. Equilibrium Dean profiles will be calculated. To do so, different mean grain diameters D 50 will be used to make this calculation. In Figure 4.11 the calculations that have been executed are summarized. Hereafter, the calculation method will be elaborated more in detail. End of groynes Distance from shore [m] Profile 2 (original bottom) Dean profile (D50 = 0.2 mm) Dean profile (D50 = 0.1 mm) Dean profile (D50 = 1 mm) Original bottom Figure 4.11: Dean shaped nourishment profiles. In Figure 4.8 three cross-shore profiles have been depicted. In Figure 4.7 the locations of these profiles have been indicated on a depth chart. As can be seen from this depth chart, the depth contours are more or less parallel. For the calculation of the equilibrium Dean profiles that will be nourished, it will be assumed that profile 2 is representative for the entire width of the project location between the two groynes. This profile has been indicated in purple in Figure Groynes The new beach will be created between two existing groynes. In combination with the floating breakwater that has to be designed, these groynes play an important role for the stability of the new beach. Together they will form a protected closed area wherein the new beach will be situated. As has been mentioned in Section 4.3.7, the groynes have a length of about 120 m. The groynes have been indicated with a blue line in Figure Dry beach width In order to make an artificial beach, a certain dry beach width (width of the beach above the water line) has to be assumed. Width the aid of GOOGLE EARTH (2010) the width of several beaches in the surroundings of the project location has been measured. Most of the beaches have a width of about 30 m. That s why in this project a dry beach width of 30 m will be taken. 99

100 Equilibrium Dean profiles beach nourishment In the conclusion of the sediment sample analysis (Section 3.7.5), several possible sediment sizes (D 50 ) for the nourishment materials have been mentioned. The following possible grain sizes will be investigated: - D 50 = 0.1 mm as lower limit of the potential borrow material. - D 50 = 0.2 mm as upper limit of the potential borrow material. - D 50 = 1.0 mm. It is possible to create sand with this mean grain diameter with the aid of a hydro cyclone, which will be used during the dredging and nourishment process. The Dean profiles follow the relation (repeated from Equation (4.21)): h( y) n Ay (4.36) In this equation n 2 3. The shape parameter A can be calculated with the following equation (repeated from Equation (4.25)): A w (4.37) The equilibrium Dean profiles corresponding to the above mentioned values for D 50 have been plotted in Figure The parameters to calculate the profiles have been summarized in Table 4.7. Table 4.7: Equilibrium Dean profiles. Mean grain diameter D 50 [mm] Fall velocity w [m/s] Shape parameter A [m 1/3 ] As can be seen in Figure 4.11, the profiles have been shifted 30 m to the right. This has been done in order to take the dry beach width into account. As can be seen, the profiles for D 50 = 0.1 mm and 0.2 mm do not intersect the original bottom. However, the profile with coarser material of D 50 = 1.0 mm intersects the existing bottom at a distance of 75 m. Distance from coast to floating breakwater The next parameter that will be investigated is the position of the floating breakwater with respect to the coastline. The problem will be explained with the aid of Figure

101 Figure 4.12: Determination of the position of the floating breakwater with respect to the coastline. The distance to the original coastline is the main variable in this section. It has been indicated in the figure. The offshore distance can be chosen arbitrarily. The original bottom and an arbitrary nourished profile have been indicated in the figure. The wave boundary condition H e,i at the seaward side of the to be designed floating breakwater, depends on the value of the effective wave height H e at a depth of 15 m, that has been calculated in Section The corresponding value at the point of the floating breakwater will be calculated as follows. The maximum potential offshore distance will be approximately 300 m from the coastline. At that distance the original water depth equals 5.8 m. The value of H e at a depth of 15 m equals 3.75 m. During the longshore transport calculations a value for the breaker parameter of γ br = 0.5 has been assumed, which indicates the maximum possible wave height at certain water depth. This means that, while the wave with a height of 3.75 m travels towards the coast, will break at a depth of approximately H 3.75 m h 7.5 m (4.38) 0.5 At a depth of 7.5 m the distance to the coastline is 450 m. It will be assumed that, in landward direction of this point, due to the process of breaking, the maximum occurring wave height H e,i at the seaward side of the breakwater will be equal to: HeI, h 0.5h (4.39) If a certain offshore distance to the location of the floating breakwater has been chosen, the nourished (Dean shaped) profile will be truncated at that location. This means that at that location the closure depth h * has to be maintained. With the aid of equation (4.28) the corresponding maximum allowed effective wave height that is transmitted past the floating breakwater H e,t can be calculated. Equation (4.28) can be rewritten the following quadratic equation: He He h* 0 gte (4.40) The roots of this quadratic equation with independent variable H e can now be solved, the lowest root is the value for H e,t to be used. For the value of the transmitted peak period T e, which is needed to solve Equation (4.40), it will be assumed that the period of the transmitted wave is equal to the period of the incoming wave. 101

102 In between the original bottom and the seaward end of the nourishment profile a transition slope will be created, if the nourished profile doesn t intersect the original bottom. Next, the required wave transmission coefficient can be calculated by dividing the incoming wave height H e,i by the maximum allowed transmitted wave height H e,t at the landward side of the breakwater. In Table 4.8, the above mention calculation procedure will be executed for the equilibrium Dean profiles from Figure Table 4.8: Calculation of distance from coastline to location of floating breakwater. D50 [mm] horiginal profile H* wave height He,T coefficient KT Mean grain diameter Distance to coast [m] Original water depth Incoming wave height He,I [m] Closure depth of Required transmitted Required transmission Remarks Conclusion At end of groynes At end of groynes Intersects existing bottom Several distances to the coast have been investigated (see Table 4.8): 120 m, which is the distance if the floating breakwater will be situated between the end points of the groynes. Furthermore 150, 200 and 250 m have been investigated. As can be seen, for the several investigated mean grain diameters, the required transmission coefficient is almost independent of the distance to the coast. An interesting point is the case with the profile belonging to D 50 = 0.2 mm. Regardless the distance to the coast, the transmission coefficient is more or less equal to 1. This would indicate that, if one uses material with a mean grain diameter of 0.2 mm, no floating breakwater is required. As was mentioned before, the profile belonging to D 50 = 1.0 mm intersects the existing bottom already at a distance of 75 m from the original coastline. For that case, the calculation was executed for the offshore distance of 75 m. From this became clear that, because of the fact that a K T higher than 1 was calculated, a profile with sand with a D 50 = 1.0 mm is stable without a floating breakwater in place. 102

103 4.6 Conclusions General conclusions In the previous sections, the cross-shore and longshore sediment transport along the beach have been investigated. Regarding the stability of the beach in combination with a floating breakwater in front of it, the following conclusions can be drawn: - If one places the breakwater closer to the shoreline, less material will be lost due to longshore transport past the tips of the groynes. - From Table 4.8 also becomes clear that, if the ready available material with a mean grain diameter of 0.1 mm will be used, a breakwater is always needed to secure the stability of the beach. - If one uses the upper boundary of the potential borrow area of D 50 = 0.2 mm, it appears that no breakwater is needed, because a transmission coefficient of 1 or higher is calculated for all distances to the coast. However, it should be noted that this is the boundary value of D 50 regarding the necessity of a floating breakwater. - From Table 4.8 becomes clear that, if one uses material with a mean grain diameter of 1.0 mm, a relative low volume of nourishment material is needed to get an equilibrium Dean profile. If one uses a mean grain diameter of 1.0 mm, no floating breakwater is needed. Whether this option is attractive, will depend on a costs and benefit analysis. However, such a cost-benefit analysis is not part of the current investigation. - It should be noted that theoretically the calculation of the incoming wave height is correct, which in the calculation is based on the linear decay in wave height due to the process of breaking. From the breaking point of the incoming wave towards the shoreline, it is assumed that the wave height is governed by the process of breaking. Hereby other local effects (such as shoaling) are neglected Distance to coastline From the result of the calculations, a suitable distance from the breakwater to the coastline has to be chosen, which will be used to calculate the optimal cross-section of the floating breakwater. In the remainder of this report, the borrow material with a mean grain diameter of 0.1 mm will be considered in the calculations. This will be done because, as appears from the results above, no floating breakwater is needed with the use of coarser material. The distance should be equal to or larger than 120 m, because of the length of the groynes. The breakwater shouldn t be placed too close to the shoreline, because of aesthetic reasons. Also, the distance shouldn t be too large, because the further away the breakwater will be placed from the shoreline, the more sand is needed for the artificial beach. As can be seen in the longshore transport calculation table from Appendix F, significant longshore transport rates occur until a distance of about 400 m from the coastline. This indicates that it is efficient to place the breakwater at a distance smaller than 400 m to the coastline, to minimize the loss due to longshore transport. Taking consideration mentioned above into account, a distance to the coastline of 200 m will be chosen. 103

104

105 Chapter 5 Wave transmission coefficient and floating breakwater type In this chapter, the required wave transmission coefficient will be calculated. Also, a floating breakwater type will be chosen, that can provide this required wave transmission coefficient. 5.1 Wave transmission coefficient Design value With the results from Chapter 2 (boundary conditions) and Chapter 4 (required wave conditions) the required wave transmission coefficient of the floating breakwater can be calculated. The wave transmission coefficient K T is defined as the transmitted wave height (H T ) divided by the incoming wave height (H I ): K T H H T (5.1) I Because this transmission coefficient is an important parameter in the design of the floating breakwater, it is mentioned in a separate section. For the overview, the required transmission coefficient will be repeated hereafter. As has been mentioned in Section 4.6, the breakwater will be placed at a distance of 200 m from the coastline. The water depth at this point equals 4.0 m. At that point, for the equilibrium Dean profile belonging to D 50 = 0.1 mm, a value for the transmission coefficient K 0.6 (5.2) T is needed Distinction between summer and winter wave conditions A distinction can be made between summer and winter wave conditions. It is to be expected that the summer wave conditions will be milder than the winter conditions. This is confirmed by the data presented in Figure 3.16g, which shows the maximum measured wave heights at the Gloria drilling platform. The maximum recorded monthly wave height during winter is much higher than the maximum recorded monthly value during summer. In winter high storm waves will occur. It can be expected, due to the conclusions that have been described in Section 3.5, that the breakwater will certainly be necessary during the severe wave conditions that will occur in winter. That s why the dimensions of the floating breakwater will be based on the winter conditions. Taking the elaboration above into account, it can be concluded that it is possible to remove the floating breakwater during summer, because the summer wave conditions are mild compared to the storm conditions that can occur in winter. 105

106 5.2 Suitable types of floating breakwaters In this section, an investigation on several available types of floating breakwaters will be made. Thereafter, a choice has to be made on what type of breakwater is the most suitable to use as breakwater to protect the proposed artificial beach. The choice that has to be made will be based on the capacity to achieve the required wave transmission coefficient K T in the occurring wave conditions and the possibility to manufacture the structure in the vicinity of the project location Types of floating breakwaters from literature In Appendix I, an overview regarding several types of possible floating breakwaters will be made. First, a way to classify the different types of breakwaters will have to be found. Next, an overview of possible types of breakwaters will be given, with an elaboration on their performance in certain wave climates Local production possibilities At September 21, 2010 the company Ship Machine Building has been visited to investigate the possibilities to produce the floating breakwater. Ship Machine Building is a company in Varna, Bulgaria which has specialized itself in producing floating structures made of Ferro concrete. During this visit, information has been gathered regarding the production possibilities. A report of this visit can be found in Appendix H. A summary of the results can be found below. Production data: - Maximum dimensions of a structure are length x breadth = 95 m x 19 m. - The draft should be less then 4.7 m, because of the water depth next of the slipway. - Maximum weight of the structure should be 1200 t. - The density of the concrete used is 2400 kg/m 3. One structure built by Ship Machine Building has been in salt water since This structure is still in good shape and undamaged. That means that the structure has been undamaged for 33 years. Production rates of 150 m 3 of concrete per day have been reached in the past. A first assumption for the construction costs per m 3 of concrete can be 900 / m Choice of type of floating breakwater In Section several types of floating breakwaters have been described. In Section the local production possibilities of floating breakwaters have been investigated. Because of the presence of a company that can produce floating caissons in the vicinity of the project location (in Varna), the type of floating breakwater that will be used for this project will be a floating caisson breakwater. 106

107

108

109 Chapter 6 Interaction between floating breakwater and beach In this chapter, the interaction between the floating breakwater and the beach will be investigated. As has been mentioned in Chapter 5, the breakwater will be a concrete pontoon floating breakwater. 6.1 First assumptions In this chapter, the following assumption are made: - To get a first indication of the interaction between the artificial beach and the floating breakwater, it will be assumed that the breakwater has a rectangular shape. - The breakwater has a position which is fixed in space. - The floating breakwater is infinitely long in longshore direction. 6.2 Transmission coefficient Global dimensions of cross-section In literature, several expressions and graphs for the transmission coefficient K T = H T /H I of a floating breakwater can be found. These expressions and graphs will be discussed hereafter. The parameters that will be used in these expressions are defined in Figure 6.1. Figure 6.1: Definition of several parameters related to the floating breakwater. The following structural parameters are used: - d = local water depth - B = breadth of the breakwater - D = draft of the breakwater - R C = freeboard of the breakwater - h = height of the breakwater (= R C + D) The following wave parameters are used: - H I = incoming wave height - L = incoming wave length - H T = transmitted wave height The length of a breakwater section (measured perpendicular to the plane of the drawing) is called l. 109

110 6.2.2 Transmission coefficient in literature Power transmission theory by Wiegel for a thin barrier A publication that is referred to in HALES (1981) is an investigation done by Ursell. The finite width of a floating structure as depicted in Figure 6.1 was taken to an infinitely small limit. For this infinitesimally thin barrier Ursell developed a theory for the partial reflection and the partial transmission of waves in deep water. The barrier extends from the water surface to some depth D. The following expression for the transmission coefficient was developed: K T I 2 D k1 L 2D 2D k L L (6.1) Where I D L and 2 2 D k1 L are modified Bessel functions. Experimental studies performed by Wiegel revealed that this theory fitted good trough data from experiments, which can be seen in Figure 6.2. Figure 6.2: Comparison of theories and experimental data for wave transmission past a fixed, rigid, vertical thin plate (HALES, 1981). Wiegel investigated the conceptual model. A theory was developed based on the assumption that the that the power being transmitted by a wave between the bottom of the vertical barrier and the sea 110

111 bottom, assuming the structure is not there, will be the power transmitted past the structure (Cited from TOLBA, 1999). Wiegel s expression for the transmission coefficient reads: K T Pt P i 4 D d L sinh 4 D d L sinh 4d L sinh 4d L 4 d L 1 sinh 4 d L (6.2) Where: P t = transmitted wave power P i = incident wave power The experiments performed by Wiegel (see Figure 6.3) demonstrated that this theory might be useful for first approximations but that improvements in the theory were needed. Figure 6.3: Effect of depth of submergence of a thin, rigid, fixed vertical plate on the transmission coefficient - experimental results and power transmission theory of Wiegel (Equation (6.2)). It should be noted that the draft is called y in this graph (HALES, 1981). In Figure 6.4 the expression of Wiegel has been displayed graphically for different values of L/d. 111

112 Figure 6.4: Visual representation of the expression of Wiegel (Equation (6.2)) for different values of L/d. It should be noted that the draft is called y in this graph (adapted from WIEGEL,1960). Macagno HALES (1981) refers to an investigation performed by Macagno. A rigid structure of finite width, height and draft (see Figure 6.1) was studied, at a fixed position with respect to the bottom. It was assumed that no overtopping took place, like the dimension (h - D) is very large. An expression for the transmission coefficient was developed. The expression reads: K T 1 2 d Bsinh L 1 2 d D L cosh L 2 (6.3) However, in PIANC (1994) has been mentioned that this model appears to be inadequate for important values of the relative draft D/d. For example, it is known that if the draft D of the breakwater is equal to the water depth d, the transmission coefficient is equal to zero. This is not predicted by Equation (6.3). HALES (1981) states that an investigation of Jones indicated that no large errors occur if small degrees of submergence are introduced. 112

113 Carr, Healy and Stelzriede In the PhD thesis of TOLBA (1999) the following study is mentioned. For the case of a rigid board of length 2B, which is fixed at the still water surface in shallow water, Stoker found the following expression, using linear wave theory: K T 1 2 B 1 L 2 (6.4) An equation for shallow water that is similar to Equation (6.4) was developed by Carr, Healy and Stelzriede. The equation included a term to express the finite draft: K T 1 2 B 1 1 L 2 S (6.5) In Equation (6.5), S the ratio of the depth of the immersed body below the still water level (D) to the vertical distance from the bottom of the body to the sea bed (d - D): Design graphs D S d D (6.6) In PIANC (1994) graphs regarding the influence of the breadth B and the draft D on the transmission coefficient can be found. These graphs are displayed in Figure 6.5. The graphs can originally be found in a publication from Jones, who created the graphs based on the above mentioned equation from Wiegel (Equation (6.2)) and the theory by Macagno (Equation (6.3)). 113

114 Figure 6.5: Graphs displaying the transmission coefficient for a fixed, rectangular surface barrier, for different values of L/d (adapted from PIANC, 1994).. Laboratory tests on fixed floating breakwaters TOLBA (1999) performed experiments with rigid fixed floating breakwaters with a rectangular cross section. For different dimensions of the structure and wave conditions the transmission coefficient has been measured. One structural parameter that has been varied is the draft D of the structure. Figure 6.6 shows the results of measured values for the transmission coefficient with varying ratio D/d of the structure. The draft D has been varied and the depth d has been kept constant. It can be observed that with increasing D (and thus increasing D/d) the transmission coefficient decreases. Another structural parameter that has been varied is the breadth B of the structure. Figure 6.7 shows the results of measured values for the transmission coefficient with varying ratio B/d of the structure. The breadth B has been varied and the depth d has been kept constant. It can be observed that with increasing B (and thus increasing B/d) the transmission coefficient decreases. The influence of the wave steepness on the transmission coefficient has also been investigated. For two values of the ratio D/d, tests have been executed for different values of the wave steepness H i /L. The results of these tests have been displayed in Figure 6.8. It can be seen that for the tested range of wave steepness the wave steepness has almost no influence on the transmission coefficient. 114

115 Figure 6.6: Variation of the transmission coefficient K T with B/L and d/l for different values of D/d. Note that the transmission coefficient is called C t in this graph. Parameter settings: B/d = 1/2, H i /L = (TOLBA, 1999). Figure 6.7: Variation of the transmission coefficient K T with d/l for different values of B/d. Note that the transmission coefficient is called C t in this graph. Parameter settings: D/d = 1/4, H i /L = (TOLBA, 1999). 115

116 Figure 6.8: The effect of the incoming wave steepness on the transmission coefficient K T for two different values of D/d. Note that the transmission coefficient is called C t in this graph (TOLBA, 1999). Similar tests as described above have been executed by KOUTANDOS et al. (2005). A fixed rectangular floating breakwater has been tested under regular and irregular incoming waves. During the tests, waves where generated covering a range of shallow and intermediate waters. The tested ratios of depth to wave length where 0.04 < d/l < The test results have been summarized in Figure 6.9 for regular waves and in Figure 6.10 for irregular waves. It can be seen that the results for regular and irregular wave forcing follow more or less the same trend. Figure 6.9: Variation of the transmission coefficient K T with B/L for different values of D/d (the draft is called dr in this figure). Regular waves have been used. Note that the transmission coefficient is called C t in this graph. Figure a gives the results for an incoming wave height H i = 0.2 m and figure b for H i = 0.3 m. Parameter settings: B/d = 1 (in the experiments B = d), 0.04 < d/l < 0.35 (KOUTANDOS et al., 2005) 116

117 Figure 6.10: Variation of the transmission coefficient K T with B/L for different values of D/d (the draft is called dr in this figure). Irregular waves have been used. Note that the transmission coefficient is called C t in this graph. Parameter settings: B/d = 1 (in the experiments B = d), 0.04 < d/l < (KOUTANDOS et al., 2005) Design parameters Hereafter, the design parameters will be repeated for overview and other required design parameters will be determined. Significant wave height regarding beach stability One important design parameter is the incoming wave height. As has been motivated in Section 4.5.1, the value of the incoming design significant wave height regarding beach stability is equal to Hs, beach design He 2.0 m (6.7) This is the significant design wave height based on the wave height that is only exceeded 12 hours per year (the effective wave height H e ). Maximum wave height wave height (single wave) regarding breakwater design The above mentioned value of H s 2.0 m is too low to design the floating breakwater itself. For the floating breakwater, the maximum occurring wave height (of a single wave) instead of significant wave height is needed. Because of the fact that at the location of the floating breakwater shallow water conditions occur, it will be assumed that one individual wave can t become higher than 0.7 times the local water depth, due to the process of wave breaking: Hmax 0.7d m (6.8) Maximum significant wave height wave height regarding breakwater design However, for some design aspects of the breakwater, like the calculation of overtopping, the value for a certain significant wave height is needed. As has been mentioned in Section 3.6.5, the maximum occurring significant wave height at the point of 15 m water depth doesn t exceed H s = 4.24 m. When waves with this value of the significant wave height travel towards the shoreline, they will start to break before they reach the location of the floating breakwater. Because of this fact, just like the case of H e, 117

118 it is assumed that the maximum occurring significant wave height does not exceed a height of half the local water depth, i.e. Wave period and wave length Hs,max Hs, design 2.0 m (6.9) As has been mentioned in Section 4.5.1, the value of incident wave period corresponding to the design wave height equals T p = 8.96 s. The corresponding wave length at the local water depth of 4 m (at 200 m distance from the coast) will be calculated by means of Equation (3.3). This wave length equals L = 54.2 m. Wave steepness The wave steepness of the incident design wave equals: Depth over wave length ratio The wave steepness of the incident design wave equals: Transmission coefficient H s 2.0 m Wave steepness (6.10) L 54.2 m d 4.0 m 0.07 L 54.2 m (6.11) The required transmission coefficient for the floating breakwater equals K T = 0.6. Maximum possible dimensions regarding production possibilities In Section the maximum size of a structure that can be produces by Ship Machine Building have been mentioned. The maximum dimensions are summarized in Table 6.1. Table 6.1: Maximum possible dimensions of the floating breakwater. Dimension Maximum value [m] Length l 95 Breadth B 19 Draft D Choice of design method and determination of required dimensions In this section, a choice on what information as described in Section will be used to determine the required dimensions of the floating breakwater. Comparison of different references In Section several references have been found on how to determine the required dimensions to achieve a certain transmission coefficient. Both analytical expressions and experimental results have been presented. Hereafter, the experimental results will be compared with the analytical expressions of Macagno (Equation (6.3)) and Carr, Healy and Stelzriede (Equation (6.5)). First the experimental results of TOLBA (1999) will be analyzed. The data as presented in Figure 6.6 for the case of B/D = 1/4 and D/d = 1/6 have been plotted in Figure 6.11, together with the corresponding 118

119 Transmission coefficient KT [-] Transmission coefficient KT [-] Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria values of the transmission coefficient as calculated by the two afore mentioned analytical expressions. As can be seen, as could be expected, when the breadth B, and hence B/L, increases, the transmission coefficient decreases for both the analytical expression as the experimental results. However, compared to the analytical results, both analytical expressions give higher values of K T then the experimental results. The expression of Carr, Healy and Stelzriede matches the experimental results well for values of B/L smaller then B/L Macagno Carr, Healy and Stelzriede Tolba (1999) B/d = 1/4 D/d = 1/6 Figure 6.11: Comparison of the experimental results of TOLBA (1999) to the analytical expressions of Macagno and Carr, Healy and Stelzriede. The data as presented in Figure 6.7 for the case of B/d = 1/2 and D/d = 1/6 have been plotted in Figure 6.12, together with the corresponding values of the transmission coefficient as calculated by the two afore mentioned analytical expressions. Both the analytical expression as the experimental results show a decreasing trend in the value of K T when the value of d/l increases. However, both analytical expressions give higher values for K T then the experimental results d/l Macagno Carr, Healy and Stelzriede Tolba (1999) B/d = 1/2 D/d = 1/4 Figure 6.12: Comparison of the experimental results of TOLBA (1999) to the analytical expressions of Macagno and Carr, Healy and Stelzriede. 119

120 Transmission coefficient KT [-] Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria In the same way, hereafter the experimental results as presented by KOUTANDOS et al. (2005) (see Figure 6.9a) have been compared in Figure As can be seen, the analytical expression of Macagno predicts higher values for the value of K T then the experimental results. On average, the expression of Carr, Healy and Stelzriede gives a good fit trough the experimental data B/L & d/l Macagno Carr, Healy and Stelzriede Koutandos et al. B/d = 1 D/d = 1/4 Figure 6.13 Comparison of the experimental results of KOUTANDOS et al. (2005) to the analytical expressions of Macagno and Carr, Healy and Stelzriede. In Figure 6.14 the analytical expression has been drawn for the design parameters of d = 4 m and L = 54.2 m. In Figure 6.14a the value for D has been kept constant at D = 1.50 m. As can be seen, with increasing breadth the value of K T decreases faster for Carr, Healy and Stelzriede then for Macagno. The graphs indicates that a breadth of about 50 m is necessary according the expression of Carr, Healy and Stelzriede, where only a value of about 7 m is needed according to Macagno, to achieve the required transmission coefficient. In Figure 6.14b the value for B has been kept constant at B = 10.0 m. As can be seen, with increasing draft, the value of K T decreases very rapidly according to the expression of Carr, Healy and Stelzriede. On the other hand, the increase of draft D has almost no influence on the transmission coefficient according to the expression of Macagno. It is interesting to note that for both expressions the graph does not start at K T = 1.0, but at lower values. This indicates that a breakwater with a certain breadth already causes damping if the draft D = 0, i.e. if the bottom of the breakwater is located at still water level. 120

121 Figure 6.14: The two analytical solutions for the design values of d = 4 m and L = 54.2 m with a: varying values of D and constant value of B and b: varying values of B and constant value of D. The dashed line indicates the required transmission coefficient K T = 0.6. The design ratio of d/l (Equation (6.11)) equals Almost none of the experiments have been performed included this value in the results. However, the available graphs with test results have been used to extrapolate to the design value of d/l. Dimensions (B and D) according to different references With the aid of the calculations method and graphs that have been described in Section 6.2.2, possible dimensions (B and D) to obtain the required transmission coefficient of the floating breakwater have been determined. They have been summarized in. In the column Reference has been indicated which equation or graph has been used to determine the required dimensions. The design graphs adopted from PIANC (1994), see Figure 6.5, can t be used to estimate the required dimensions, because the design value of L/d is outside the range of the available graphs in Figure 6.5. Table 6.2: Possible dimensions of the floating breakwater to achieve the required K T = 0.6. Reference Breadth B [m] Draft D [m] Analytical expression of Macagno, see Equation (6.3) Analytical expression of Carr, Healy and Stelzriede, see Equation (6.5) Experimental results from TOLBA (1999), see Figure Experimental results from KOUTANDOS et al. (2005), see Figure As can be seen from the table, there is a lot of variation between the reference sources. Because of the fact that the results of the tests don t lie within the range of design parameters, it s difficult to assess which analytical expression will give a reliable estimation of the required transmission coefficient. On the other hand, experiments may be more reliable then analytical expression. This is 121

122 because of the fact that with experiments data have been measured in reality and an analytical expression is just a model of reality. As can be seen in Table 6.2 and in Figure 6.14b, for the expression of Macagno, for a constant value of breadth B, a change in draft D has almost no influence on the value of the transmission coefficient. With the expression of Carr, Healy and Stelzriede, there is a clear influence of the draft D on the transmission coefficient. Also, as already mentioned in Section 6.2.2, in PIANC (1994) is stated that the expression of Macagno does not take into account the fact that that the transmission coefficient should be equal to zero in the case of D/d = 1, i.e. if the draft is equal to the local water depth. Because of these reasons, the expression of Macagno will be disregarded in this study. If the results of the extrapolation of the experimental results from TOLBA (1999) and KOUTANDOS et al. (2005) are being reviewed, one can see that both references give values of the same order of magnitude for the variables B and D. If one compares these results to the results in the yellow coloured of the analytical solution of Carr, Healy and Stelzriede, it appears that these values have the same order of magnitude as the values interpolated from the experimental results. Frome these values can be concluded that the main factor causing the wave damping is the draft D of the structure. The breadth is not the main factor that causes the damping. However, the breadth is an important factor to assure the stability of the breakwater. In the remainder of this report, the following value of the draft will be taken: D 2.5 m (6.12) The description above indicates that the breakwater can be designed (regarding draft D) as a wave screen, which protrudes the water surface until a certain draft D. To verify this, the expression by Wiegel (Equation (6.3)) for an infinitesimally thin barrier (wave screen) can be used to determine the draft that is needed to obtain a transmission coefficient equal to 0.6. In Figure 6.4, Equation (6.3) has been displayed graphically for different values of d/l. In Figure 6.4 can be seen that for the design value of d/l = 0.07, for a K T = 0.6, the required value for D/d = With the design depth d = 4.0 m follows that a draft D = 2.5 is needed. This is exactly the same value as has been chosen in Equation (6.12)) Problem description The design problem has been illustrated in Figure The necessary draft calculated in Section equals D = 2.5 m. This value has been calculated under the assumption that the floating breakwater is fixed in space. In to order fix the breakwater as much as possible in space, the mooring lines have to be always tight, i.e. the mooring system is pre-tensioned. As has been mentioned in Section 6.2.3, the wave length of the design wave equals 54.2 m and the maximum wave height 2.4 m. A wave length and trough have been indicated in Figure In both the trough and the crest, the mooring lines should be tight. The draft D = 2.5 m and the under keel clearance D - d = 1.5 m are fixed values. The values for breadth B and freeboard R C have to be determined. Hereafter, the design problem will be solved step by step. Design conditions The breakwater design should satisfy the following conditions: - On the one hand, the breakwater has to be designed in such a way that it has enough buoyancy to keep the mooring lines tight in the design wave trough, meaning that in that situation the weight of the floating breakwater is not allowed to exceed the buoyancy force. This situation has been illustrated in Figure 6.16a. 122

123 - On the other hand, the breakwater should have enough buoyancy to keep the mooring lines tight in the design wave crest. This situation has been illustrated in Figure 6.16b. - The breakwater should be stable during free-floating conditions while transporting it (during relatively calm weather). - The freeboard R c with respect to still water level should be sufficiently large to reduce overtopping to a minimum. Figure 6.15: Explanation of the design problem. Figure 6.16: Floating breakwater in design wave trough level (a) and design wave crest level (b). Freeboard The freeboard of the floating breakwater should be sufficiently high in order to minimize overtopping. To calculate the required freeboard, the floating breakwater can be schematized as a vertical wall caisson breakwater. The computer program Breakwat (BREAKWAT, 2005) has a routine to calculate the 123

124 wave transmission for different values of the freeboard. This routine has been described in Appendix J. Setting of input parameters: - H s,i = 2.0 m The program asks for values of α and β. These parameters depend on the type of structure. Since for the calculation of transmission due to overtopping the floating breakwater can be modelled as a vertical caisson breakwater, the values for α and β are set at: - α = β = 0.40 These values can be found in the help file of Breakwat (see also Appendix J). For different values of the freeboard, the transmitted wave height due to only overtopping is listed in Table 6.3. Table 6.3: Calculation results of transmitted wave height duet o overtopping for different values of the freeboard R C, calculated with (BREAKWAT, 2005) Freeboard R c [m] Transmitted wave height (due to overtopping water) H s,t [m] Transmission coefficient K T (due to overtopping water) As can be seen, with a freeboard of 2.5 m, the transmitted wave height equals only 7 cm. This value seems acceptable. That s why a value of R c = 2.5 m will be chosen (marked with orange in Table 6.3). Wall thickness The to be designed floating breakwater will consist of floating Ferro-concrete caissons. A wall thickness t = 100 mm = 0.1 m of the caisson will be taken. This value has been taken from a drawing of a floating breakwater that already has been constructed by Ship Machine Building. Breadth The situation that will determine the dimensions to assure that the mooring lines are always tight, i.e. the situation that governs the minimum needed buoyancy, is the situation when the floating breakwater is situated in a trough of the design wave H max, see Figure 6.16a. 124

125 Figure 6.17: Floating breakwater in design wave trough level, explanation on the calculation of breadth B. The breadth B will be calculated for this situation, by means of a calculation under the assumption that the floating breakwater is free floating in the design wave trough level, with the design under keel clearance D - d = 1.5 m, see Figure In this situation, the draft equals (D - ½ H max ) = 1.3 m. To calculate the breadth, the static stability of this free floating situation will be investigated. First, the positions of the centre of mass (G) of the cross section and the centre of pressure (B) of the part of the cross-section below the water line will be determined. The positions of these points have been indicated in Figure It should be noted that the breadth and the centre of pressure both have the symbol B. Next, the breadth will be chosen in such a way that the so called meta centre M is situated above G. In this way it is assured that a corrective moment is generated in case of a small tilt of the element, assuring the element to return to its initial neutral position. The distance BM is called the metacentric height h m. For details on the calculation of the position of the meta centre is referred to basic literature on ship stability. The distance BM can be calculated by: BM I V (6.13) Where: I = the moment of inertia, relative to the central axis of the floating breakwater element (perpendicular to the plane of Figure 6.17), of the area that cuts the waterline [m 4 ] V = the displace volume of water by the floating breakwater element [m 3 ] I and V can be calculated as follows: I B (6.14) 1 2 max V B D H (6.15) By substituting Equations (6.14) and (6.15) into Equation (6.13), the following expression is obtained: 125

126 BM B 1 12 D 2 Hmax 2 (6.16) The metacentric height h m can be calculated by: hm GM BM BG (6.17) With the aid of Equations (6.16) and (6.17), for a certain value of h m, the required value of the breadth can be calculated. The value of BG is 1.8 m, see Figure This means that BM should be larger then 1.8 m, in order to assure the static stability. A value for h m = 0.5 m is chosen. From Equations (6.16) and (6.17) can now be calculated that the needed breadth amounts B = 8.0 m. This value for the breadth will be used in the design of the breakwater. When the floating breakwater is in place, it will be restrained to a certain extend to move, by means of a pre-tensioned mooring system. This means that the above calculated breadth (in free-floating conditions) will be enough to assure the stability in restrained conditions. Check of weight versus buoyancy In this section, all the calculated volumes and forces have a unit per running m of breakwater. Buoyancy in design wave trough level With the above calculated value of B, the required buoyancy force to keep the breakwater sections floating (in the situation of the design wave trough level) can be calculated, see Figure 6.16a. The buoyancy force in trough level F B,trough. can be calculated as follows: 1 B, trough w 2 max F g D H B (6.18) Where: F B,trough = the moment of inertia, elative to the central axis of the floating breakwater element [N/m 1 ] ρ w = density of water [kg/m 3 ]. g = gravitational acceleration [m/s 2 ] In Section 4.4 the sea water density has been determined to be ρ w = 1011 kg/m 3. However, in the following calculations, a water density of ρ w = 1000 kg/m 3 has been used to get an indicative value of the occurring buoyancy force. With the above calculated values for D and B, the buoyancy force becomes F B,trough. = kn/m 1. Buoyancy in design wave crest level In the same way, the required buoyancy force in the design wave crest F B,crest (where the water level is elevated with half the maximum wave height) can be calculated, see Figure 6.16b. This can be done with the following expression: 1 B, crest w 2 max F g D H B (6.19) With the above calculated values for D and B, the buoyancy force becomes F B,crest. = kn/m 1. Weight of the structure In Figure 6.18 the designed cross-section has been displayed, width the dimensions B x h and wall thickness t. 126

127 Figure 6.18: The designed cross section of the floating breakwater. The area of the cross section of concrete A concrete of this element can be calculated with the following expression: concrete total hollow part 2 2 A A A hb h t B t (6.20) The weight per running m of breakwater F G can be calculated by multiplying the area of concrete in the cross-section A concrete by the density of the concrete used ρ s (= 2400 kg/m 3, see Section 5.2.2) and the gravitational constant: F A g G, cross section concrete c (6.21) The weight of the floating breakwater cross section per running m was calculated to be F G,cross-section = 60.3 kn/m 1. To assure the structural stability of the pontoon itself, stabilization walls will be placed every 4 m, measured in longitudinal direction. These walls will also have a thickness t = 0.1 m. The weight of one wall can be calculated. Next, by dividing this weight to the centre to centre distance of the walls, the weight per running meter of breakwater due to the presence of stabilization walls can be calculated: F G, walls V 2 2 wall B t h t cg cg (6.22) center to centre distance center to centre distance With the values of the variables mentioned above, the weight per running m of breakwater due to the walls was calculated to be F G,walls = 22.0 kn/m. The total weight per running meter of breakwater is then equal to: F F F 1 G G, cross sec tion G, walls 82.3 kn/m (6.23) 127

128 Conclusion Summarizing, the minimum buoyancy force (in wave trough), the maximum buoyancy force (in wave crest) and the weight of the caisson are: F B,trough. = kn/m 1 F B,crest. = kn/m 1 F G = 82.3 kn/m 1 From these numbers becomes clear that the designed breakwater cross section is light enough to keep floating in both the crest and trough level. Sideward directed wave force When a wave approaches the floating breakwater, a horizontal force F wave will be exerted on the side of the floating breakwater elements. To verify if the designed cross section in combination with the mooring system is stable under this wave load, a calculation regarding this stability will be made. With the aid of the computer program Breakwat (BREAKWAT, 2005), the force that is exerted by an incoming wave can be calculated. The program is based on a vertical caisson breakwater, but can also be used in the situation of a floating breakwater, because the exerted wave force will be the same in both situations. The calculation procedure can be found in Appendix J. The schematized force scheme used by Breakwat has been displayed in Figure Figure 6.19: Schematized force scheme used by Breakwat, to calculate the incoming wave force (BREAKWAT, 2005). With Breakwat was calculated that the incoming wave force, belonging to the design wave height H max, equals F wave = 94.2 kn/m 1. Now, the following situation will be investigated. The incoming wave is the design wave as described earlier. At the moment the crest of the wave approaches the structure, the horizontal wave force F wave will be equal to the earlier mentioned value of F wave = 94.2 kn/m 1. The water level around the structure will be assumed to be equal to the crest water level, MSL +1.2 m. This is assumption is a bit conservative, since in reality the water level won t be equal on both sides of the breakwater, due to the wave damping effect of the breakwater itself. However, as will become clear later, enough margin is present regarding the tension of the mooring lines to overcome this problem. This means that the occurring buoyancy force will be equal to the earlier calculated buoyancy force in the wave crest F B,crest = kn/m 1. It can be assumed that the breakwater, under the influence of wave load F wave, tends to turn around point A, which is one of the attachment points of the mooring system. This situation has been displayed in the force scheme of Figure By taking the sum of moments around point A to be equal to zero, the mooring force on the right side mooring line can be calculated (F mooring,2 ). 128

129 Figure 6.20: Force scheme to check the stability of the floating breakwater element under sideward wave attack. The forces have the following values: F wave = 94.2 kn/m 1 F B,crest = kn/m 1 F G = 82.3 kn/m 1 The sum of moments can now be calculated (clockwise rotation has been taken positive): T A F wave 2.2 m F G 4.0 m F B, crest 4.0 m F mooring,2 8.0 m 0 (6.24) By solving Equation (6.24) can be found that the mooring force on the right side mooring line F mooring,2 = 78.1 kn/m 1. This value is positive, indicating that the mooring force is still tensioned in this situation. With vertical force balance can be calculated that F mooring,1 = kn/m 1. This indicates that this mooring line is also tight. It can thus be concluded that the designed cross section with mooring system is stable under wave attack, because both mooring lines stay tight during in this situation. Stability of floating breakwater during transport Now, the stability of the floating breakwater section in free floating conditions (for example during transport) will be checked. This will be done by means of a static and a dynamic stability check. In Figure 6.21 the floating breakwater section has been displayed in free floating conditions. 129

130 Figure 6.21: Floating breakwater during transport in free floating conditions. The draft during free floating conditions D free floating can be calculated by reasoning that in free floating conditions the draft is determined by the fact that the generated buoyancy force (the weight of the displaced water volume) is equal to the weight of the floating structure. Therefore, the D free floating can be calculated as follows: D free floating F G, total (6.25) B g w By substituting the numerical values in this expression, the free floating draft appears to be D free floating = 1.0 m. The static stability check involves the check if the meta centre M is located above the centre of gravity G. This procedure has been described earlier. In the same way as described when calculating the necessary breadth, it can be derived that the value for BM can be calculated by: BM B 2 (6.26) 12 Dfree floating With the aid of Equation (6.26), the value of BM was calculated to be 5.3 m. The distance BG = 2.0 m, see By subtracting these values, the value of h m is obtained: h m = 3.3 m. This value indicates that M is located above G, so the floating breakwater is statically stable in free floating conditions. For the dynamic stability check, the natural period of oscillation of the floating breakwater element will be considered. The natural period of oscillation T 0 should be much larger then the occurring wave period during transport. T 0 can be calculated with the following expression: T 0 2 r g (6.27) gh m 130

131 Where: r g = the radius of gyration of the element about the longitudinal axis trough the centre of gravity of the element [m] g = gravitational acceleration [m/s 2 ] h m = metacentric height [m] The radius of gyration can be calculated by means of: 2 2 Bh rg (6.28) 2 3 The radius of gyration for the floating breakwater element equals r g = 2.7 m. The corresponding value for T 0 = 3.0 s. This value is too low compared to the expected (calm weather) wave period that occurs during transport. To overcome this problem, the floating breakwater can be ballasted with water during transport. To do so, a submersible pump should be incorporated in the design of the floating breakwater elements, in order to pump water in and out of the elements. Length of the floating breakwater sections and plan form layout Until now the cross section of the breakwater has been described. In this section, a plan form layout of the floating breakwater will be designed. This should be done in such a way, that the entire gap between the tips of the two groynes is covered by the floating breakwater. The distance between the two groynes amounts approximately 230 m. The maximum length of a floating breakwater section that can be constructed by Ship Machine Building amounts l = 95 m. Regarding these considerations, it is chosen to cover the gap with three coupled floating breakwater sections, which each have a length of l = 80 m. This layout has been illustrated in Figure Figure 6.22: Top view layout of floating breakwater. 131

132 6.3 Mooring forces and mooring system In this section, possible mooring systems will be described. Thereafter, the occurring mooring forces will be calculated. At last, the most suitable mooring system will be chosen Possible mooring systems Basically, a mooring system consists of two parts: anchor points at the bottom and mooring lines that connect the breakwater to the bottom of the sea. Mooring lines can be made of chains or steel cables, or a combination of these two (MCCARTNEY, 1985). Several methods to create anchor points on the sea bottom. One of them is the use dead weight anchors, such as a concrete block or a ship anchor. This method of anchoring has been displayed in Figure Figure 6.23: Anchor and line (MCCARTNEY, 1985). Another method is to drill piles into the firm rock bottom (if present) below the sedimentary layer and connect the mooring lines to the top of these piles. This method has been displayed in Figure Figure 6.24: Stake pile and line (MCCARTNEY, 1985). A third method is the use of embedded suction anchors. An embedded suction anchor is displayed in Figure It is installed by means of a suction pile (KWAG et al., 2010). This type of anchor can only be used if the bottom consists of sand or mud. The thickness of this layer should be sufficient, in order to prevent the anchor to be undermined due to erosion. More information on the installation, design and use of embedded suction anchors is referred to a paper by KWAG et al. (2010). 132

133 Figure 6.25: Photo of embedded suction anchor (KWAG et al., 2010) Mooring forces As has been mentioned earlier, the floating breakwater and mooring system have to be designed in such a way that the mooring lines are always tight. The largest mooring force will occur in case of a crest of the design wave height passes the breakwater, see Figure 6.16b. In this case, the maximum buoyancy force will be exerted on the floating breakwater. The mooring system has to counteract this buoyancy force. In Section the buoyancy force F B,crest. and the weight of the floating structure F G per running m of breakwater have been calculated: F B,crest. = kn/m 1 F G = 82.3 kn/m 1 In this chapter has been decided to create breakwater sections with a length l = 80 m. By multiplying the forces per running m to the length l of a breakwater section, the total force per breakwater section can be calculated: F F B, crest, total B, crest G, total F F G kn/m 80 m kn kn/m 80 m 6584 kn (6.29) As F B,crest is directed upwards and F G is directed downwards, per floating breakwater section, the mooring system has to resist a downward force F mooring,total equal to: Fmooring, total FB, crest, total FG kn (6.30) Each breakwater section can be equipped with eight mooring lines and anchor, on each side of the breakwater four. This means that the mooring force per anchor F mooring,anchor will be equal to: 133

134 Fmooring, total Fmooring, anchor 2100 kn (6.31) 8 However, in above mentioned calculation has been assumed that the water level is steady. As has been calculated in Section (see Figure 6.20), there is also a dynamic load on the mooring lines. The largest occurring mooring force, when a wave approaches the breakwater, was the force on the left side mooring lines, which was calculated to be equal to F mooring,1 = kn/m 1. Because one breakwater section is 80 m long and at each side of the breakwater there are four mooring lines, the mooring force for one mooring line equals F mooring, anchor F kn 80 m 2280 kn 4 4 mooring,1 (6.32) This indicates that the assumption that a steady water level equal to crest level gives a too low value for the mooring force. The design mooring force will be taken to be the value calculated in Equation (6.32), F mooring,design = 2280 kn Choice of suitable mooring system A choice regarding the connection between the bottom and the breakwater (such as a chain or a cable) and the method of fixing theses lines to the bottom has to be made. The mooring system should be able to resist the occurring mooring forces. Also, the mooring system should be suitable to install in the local conditions of the sea bottom. The mooring system should be designed in such a way, that the breakwater will be more or less fixed in space. Hereafter, per anchoring method will be described if the method is suitable for the governing conditions at the project location. - Dead weight anchors: this type of anchoring is a viable option, if the dimensions of the concrete anchor block needed stay inside certain production limits. If one assumes a thickness of a anchor block of 0.6 m, which is equal to the sediment layer thickness at the location of the floating breakwater, the other two dimensions (length and breadth) should be equal to 12.7 m, in case of a square block. These dimensions are too high to be economically attractive to produce. That s why, in this case, dead weight anchors are no viable option. - Piles: below the sediment layer a firm rock bed is present. Because of this fact, the use of piles is a possible option. However, in this report won t be investigated what the dimensions of a pile should be to resist the mooring force. In follow up studies, references involving this subject have to be consulted. - Embedded suction anchors: as has been mentioned before, for the use of this anchor type, a sediment layer of sufficient thickness is necessary. In Figure D.1 in Appendix D a map has been displayed with the measured sediment layer thickness. At the planned location of the future floating breakwater, the sediment layer thickness amounts only about 0.6 m. This layer is too thin in order to apply embedded suction anchors. That s why the use of embedded suction anchors is no possible option. Taking into account the above mentioned considerations will be chosen to use piles as anchors for the mooring system. Each of the anchors has be able to resist a load of F mooring,design = 2280 kn. However, as mentioned, a method has to be found on how to calculate the required dimensions of a pile. In the next chapter the final layout of the mooring system will be presented. 134

135 6.4 Plan form considerations In this section, the designed cross section from Section 6.2 will be taken, to describe the threedimensional performance of the breakwater. The plan form (top view) of the situation will be discussed, see Figure Currents that will develop behind the breakwater will be described qualitatively. In relation to this, it will be verified whether the quality of the water in the course of time will be sufficient Currents behind the breakwater Currents behind the breakwater are governed by the amount of water that will be exchanged with the open sea under the influence of incoming waves. Since in the Black Sea almost no tidal variation occurs, no significant tidal currents are expected behind the breakwater. As described in Chapter 6, the gap between the groynes will be covered by the floating breakwater. As a consequence, only a relatively small gap compared to the total water depth is present between the bottom of the breakwater and the sea bottom. That s why not so much water will flow into the project location as would be the case without the breakwater in place. In Figure 6.22 the top view of the situation has been displayed. As can be seen, between the tips of the groynes and both ends of the breakwater, no structure is present. However, it is expected that not much water exchange will occur via these lateral boundaries of the project location, because most of the waves will approach the coast (and breakwater) almost perpendicular, because of the effect of refraction. In case of a regular or submerged breakwater, a circulation pattern will occur behind it. With the case of this floating breakwater, it is expected that, because of the presence of the gap over the entire length of the breakwater, a more or less back and forth current pattern will develop, with the main currents directed perpendicular to the shoreline Water quality The quality of the water at the project location is important. Because of the presence of the beach, the quality should be good, because people will be swimming in the water. Mostly in summer, water quality problems are likely to occur, because of higher occurring temperatures. The water quality is closely related to the exchange of water with the open sea, stagnant water should be prevented. The presence of a floating breakwater will diminish this water exchange to a certain extend. However, as has been mentioned in Chapter 5, because of the difference in wave conditions during summer and winter, the breakwater is not necessary to assure the beach stability in summer. That s why, because of the absence of the floating breakwater in summer, no water quality problems are expected. 135

136

137 Chapter 7 Preliminary design In the previous chapters, several analytical elaborations and calculations have been made on various aspects, to come to a preliminary design of the artificial beach which is protected by a floating breakwater. The results of these chapters have been summarized for practical use in the following figures. In Figure 7.1 the designed beach in combination with the floating breakwater can be seen. The dry beach width is 30 m and the beach has a length of approximately 250 m. The distance between the original coastline equals 200 m. Three breakwater sections, each with a length of 80 m, will be placed in series to form the complete breakwater. The entire breakwater has a length of 240 m. Figure 7.1: Top view of artificial beach with floating breakwater in place. Figure 7.2 displays a cross section of the designed beach and floating breakwater. The location of this cross-section has been indicated in Figure 7.1 with A-A. The new bottom profile has been displayed with a continuous line. It should be noted that the horizontal and vertical scales are different in Figure 7.2. By calculating the area of the cross section of the beach nourishment in Figure 7.2 and multiplying this with the length of the beach (250 m), the volume of sand needed can be calculated. The amount of sand needed amounts approximately 91,000 m 3. In Appendix K a rough estimation of the amount of available sand between the -4 m and -8 m depth contour has been made. This amount was calculated to be 323,000 m 3. As has been mentioned in Section 3.7.5, approximately 25% of the sediment will be lost during the dredging process. After taking into account these losses, the effective amount of available sand is 242,000 m 3. This means that enough material is available to create the new artificial beach. 137

138 Figure 7.2: Cross-section of the final situation with the shape of the artificial beach and the floating breakwater in place. It should be noted that the horizontal scale is different then the vertical scale. The location of this cross-section has been indicated in Figure 7.1 with A-A. Figure 7.3 displays the designed side view of the breakwater. The local water depth amounts 4 m. Both the draft and freeboard of the caisson are 2.5 m. The breadth is 5 m. The distance between the bottom of the structure and the sea bottom equals 1.5 m. The wall, ceiling and bottom thickness amounts 0.1 m. As can be seen, on top of the form rock layer, a sediment layer of about 0.6 m is present. It is suggested that the anchor point (in case of piles) is situated just above the rock layer. Figure 7.3: Side view of the floating breakwater. In Figure 7.4 the top view of one floating breakwater section has been displayed. In longitudinal direction, every 4 m a stabilization wall has been placed. On each side of the breakwater section, four mooring lines will be present. 138

139 Figure 7.4: Top view of one floating breakwater section with the mooring system. 139

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141 Chapter 8 Conclusions and recommendations In this chapter, the main conclusions of this research will be presented. Also, recommendations for further study and research will be given. 8.1 Conclusions General conclusion The purpose of this study was to investigate if it is technically feasible to use a floating breakwater to protect a new artificial beach in Balchik, Bulgaria. The general conclusion drawn at the end of this study is that the use of a floating breakwater to protect an artificial beach is technically feasible. This conclusion will be further elaborated in the following section Sub-conclusions The type of floating breakwater that has been chosen is a concrete caisson floating breakwater. The main reason for this choice is the presence of a company that can produce floating concrete structures in the vicinity of the project location. Other reasons to choose for a floating breakwater instead of a fixed structure are: - Regarding the administrative regulations in Bulgaria it is easier to obtain a mooring permit (which is needed in case of a floating breakwater) then a construction permit (which is needed in case of a fixed structure). - A floating breakwater can be removed in summer, which is advantageous regarding aesthetic reasons. Regarding the native bottom profile, it was concluded that it is not stable, as the equation description by Dean did not coincide with the current bathymetry. Continuously, sediment is expected to be transported offshore. Regarding nourishment material to create the new beach, materials with several different mean grain diameters have been investigated. It was checked whether a floating breakwater is necessary to assure the stability of the artificial beach. Three mean grain diameters have been checked: - D 50 = 1.0 mm: For this diameter, no floating breakwater is needed. The material is so coarse that the equilibrium Dean profile intersects the original bottom at a relative short distance from the shoreline, indicating that this profile is stable without a floating breakwater. However, if this sediment has to be created from the local available bottom material, a lot of material will be lost, due to the separation process in a coarse fraction and a fine fraction. Another source for this sand might be a nearby inland quarry. - D 50 = 0.2 mm: For this diameter it was also found that no floating breakwater is necessary, regardless the distance of the offshore edge of the nourishment profile. However, it should be noted that this is the boundary value of D 50 regarding the necessity of a floating breakwater, so one should act careful regarding the decision whether to place a breakwater or not with the use of this sand. 141

142 - D 50 = 0.1 mm: For this diameter it was found that a floating breakwater is necessary to assure the stability of the beach. The advantage of the use of this material is that it can be dredged from the local sea bottom in the vicinity of the project location. If this material is used, approximately 25% of fines will be lost in the dredging process. From this can be concluded that the final decision on what kind of nourishment material to use will depend on a cost-benefit analysis. To investigate what dimensions a floating breakwater should have, a further investigation has been performed with the assumption that sediment of D 50 = 0.1 m will be used to create the beach. Regarding dimensions, it was found that the main parameter determining the wave transmission (for this particular case, regarding governing wave climate and governing site conditions) is the draft of the structure. The breadth of the structure is determined by the stability of the structure. 8.2 Recommendations Recommendations for follow-up studies The following recommendations for further investigations and research can be given: - In this study, diffraction diagrams and a one-dimensional wave model have been used to determine the near shore wave climate. In a follow-up study, it is advised to perform a study with the two-dimensional version of the wave model SWAN, in order to obtain a more refined near shore wave climate. - In a follow-up study, it is advised to perform physical model tests, in order to investigate the behaviour of the floating breakwater under wave attack. One of the parameters that should be measured during these tests is the transmission coefficient. In this study, it has been assumed that the floating breakwater is always fixed in space. This assumption is satisfactory for the main outlines of a preliminary design, but during detailed design the elasticity of the mooring system should be taken into account. The other parameter to be determined is the exact force in the tensioned mooring system. During these physical model tests, attention should be paid to the scaling of the elasticity of the mooring system. - With the results of the physical model tests, the design of the artificial beach can be refined more. More values for the mean grain diameter D 50 can be investigated. Also, the possibility to use a two layered system of beach nourishment can be considered (in this case a fine sub layer is protected by an armour layer of courser sand). - In this study, one specific location (regarding offshore distance) has been investigated, to asses the general feasibility of the use of a floating breakwater for beach protection. In a follow-up study, it can be investigated if a more efficient offshore distance can be found. - In this report, a functional design for a floating breakwater has been made. The constructive aspects of the caisson have not been investigated. In a follow-up study, it has to be verified whether a caisson with the assumed density of concrete is really strong enough to be built. - With the results of the above mentioned recommendations, several alternative designs can be made. With the aid of a cost-benefit analysis can be determined which alternative is the most attractive one. When calculating the costs of the alternatives, the yearly sediment losses and the renourishment period should be taken into account. 142

143 8.2.2 Recommendations regarding construction Regarding the construction of the floating breakwater, the following recommendations can be given: - In this study, only global dimensions of the breakwater sections have been determined. In a detailed design, special attention should be paid to the connection points of the mooring lines, see Figure 7.3 and Figure Further research to the application of piles as anchoring system has to be done, in order to determine the necessary dimensions of the piles. 143

144

145 References ARGOSS (2010) Description of wave and wind statistics database. Available at services [Accessed at June 4, 2010] BREAKWAT (2005) Version 3.1.1, June WL Delft Hydraulics, Delft, The Netherlands BOSBOOM, J. AND STIVE, M.J.F. (2010) Coastal Dynamics 1, Draft version February-March 2010, Lecture notes CT4305 Part 2. VSSD, Delft, The Netherlands BRUCHEV, I., DOBREV, N., FRANGOV, G., IVANOV, P., VARBANOV, R., BEROV, B., NANKIN, R., KRASTANOV, M. (2007) The landslides in Bulgaria - factors and distribution. Geologica Balcanica, Vol. 36, Issue 3-4, pp COMAN, B. (2004) EUROSION Case Study Mamaia (Romania). Available at: CRESS (2010) Coastal and River Engineering Support System, version Netherlands Ministry of Public Works (Rijkswaterstaat), IHE-Delft and TU-Delft, The Netherlands. Downloadable from d Angremond, K., Van Roode, F.C. and Verhagen, H.J. (2008) Breakwaters and closure dams, 2 nd edition. VSSD, Delft, The Netherlands DEAN, R.G. (1991) Equilibrium Beach Profiles: Characteristics and Applications. Journal of Coastal Research, Vol. 7, Issue 1, pp DEAN, R.G. (2002) Beach Nourishment - Theory and practice. World Scientific, Singapore FOOSE, R.M. AND MANHEIM, F. (1975) Geology of Bulgaria: a review. The American Association of Petroleum Geologists Bulletin, Vol. 59, Issue 2, pp FORT EUSTIS (2011) Information about sea states. Available at [Accessed at January 25, 2011] HALES, Z.L. (1981) Floating Breakwaters: State-of-the-Art Literature Review. U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Technical Report No. 81-1, Fort Belvoir, Virginia, USA HOLTHUIJSEN, L.H. (2007) Waves in oceanic and coastal waters. Cambridge University Press, Cambridge, UK HWANG, C.H. AND TANG, F.L.W. (1986) Studies on fixed rectangular surface barrier against short waves. Proceedings 20 th Coastal Engineering Conference, Taipei, Taiwan, pp IO-BAS (2010 AND 2011), System for sea environment monitoring. Available at [Accessed at September 15, 2010 and January 31, 2011] 145

146 KOUTANDOS, E., PRINOS, P., GIRONELLA, X. (2005) Floating breakwaters under regular and irregular wave forcing: reflection and transmission characteristics, Journal of Hydraulic Research, Vol. 43, No. 2, pp KWAG, D.J., CHO, I.H., BANG, S. AND CHO, Y. (2010) Embedded Suction Anchors for Mooring of a Floating Breakwater. Journal of Offshore Mechanics and Arctic Engineering, Vol. 132, Issue 2, May 2010, pp. 1-5 MAHERAS, P., TOLIKA, K. AND CHIOTOROIU, B. (2009) Atmospheric circulation types associated with storms on the Romanian Black Sea coast. Application of a new automated scheme. Studia Universitatis Vasile Goldis Arad, Seria Stiintele Vietii, Vol. 19, Issue 1, pp MCCARTNEY, B.L., (1985) Floating Breakwater Design. Journal of Waterway, Port, Coastal and Ocean Engineering, Vol. III, Issue 2, pp MULDER, A. AND VERWAAL, W. L.H. (2006) Lecture notes CT5320 Soil Mechanics - Test Procedures, version August Delft University of Technology, Delft, The Netherlands OFUYA, A.O. (1968) On floating breakwaters. C.E. Research Report No. 60, Department of Civil Engineering, Queens University, Kingston, Ontario, Canada ÖZSOY, E. AND ÜNLÜATA, Ü. (1997) Oceanography of the Black Sea: a review of some recent results. Earth-Science Reviews, Vol. 42, pp PIANC (1994) Floating Breakwaters; A Practical Guide for Design and Construction. PTC II, Report of Working Group no. 13, Supplement to Bulletin 85, Permanent International Association of Navigation Congresses (PIANC) PILARCZYK, K.W., MISDORP, R., LEEWIS, R.J. AND VISSER, J. (1986a) Strategy to erosion control of Dutch estuaries. Proceedings Third International Symposium on River Sedimentation, University of Mississippi, pp PILARCZYK, K.W., VAN OVEREEM, J. AND BAKKER, W.T. (1986b) Design of beach nourishment scheme. Proceedings 20 th Coastal Engineering Conference, Taipei, Taiwan, pp RUSU, E. (2009) Wave energy assessments in the Black Sea. Journal of Marine Science and Technology, Vol. 14, Issue 3, pp SAVOV, B. (2005) Integrated management of waterfront infrastructure of the town of Balchik with respect to the needs of tourism in the hinterland, Preliminary Works Design. Black Sea Coastal Association, Varna, Bulgaria SHIMODA, N., MURAKAMI, N., AND IWATA, K. (1991) Beach erosion control by submerged floating structure. Proceedings 22 nd Coastal Engineering Conference 1990, Delft, The Netherlands, pp SHUIKSKY, Y.D. (1993) The general characteristic of the Black Sea coasts. In: Coastlines of the Black Sea, Kos yan, R. (ed.), American Society of Civil Engineers, New York, USA, pp

147 SLABAKOVA, V., ANDREEVA, N., EFTIMOVA, P. AND NEDKOV, R. (2009) Evaluation of QuikSCAT wind vector performance with respect to field measurements for the Bulgarian part of the Black Sea. Proceedings 4 th International Conference on Recent Advances Space Technologies, pp SPM (1984a) Shore Protection Manual, Fourth Edition, Volume I. Department of the army, Waterways Experiment Station, Corps of Engineers, Coastal Engineering Research Center (CERC) SPM (1984b) Shore Protection Manual, Fourth Edition, Volume II. Department of the army, Waterways Experiment Station, Corps of Engineers, Coastal Engineering Research Center (CERC) STANCHEVA, M. AND MARINSKI, J. (2007) Coastal defence activities along the Bulgarian Black Sea coast - methods for protection or degradation? Proceedings Coastal Structures 2007, Venice, Italy, pp SUNAMURA, T. AND HORIKAWA, K. (1974) Two-dimensional beach transformation due to waves. Proceedings 14 th Coastal Engineering Conference 1974, Copenhagen, Denmark, Vol. 2, pp SWANONE USER MANUAL (2009), Version of , Delft University of Technology, Delft, The Netherlands. Available at: THEMAP 10VR 3D (2005) Version: Digital Nautical Chart. Chartworks Holland B.V., Den Helder, The Netherlands TOLBA, E.R.A.S. (1999) Teil 1: Behaviour of Floating Breakwaters under Wave Action. In: Fachbereich Bauingenieurswesen, Lehr und Forschungsgebiet Wasserbau und Wasserwirtschaft, Bericht Nr. 11, Kaldenhoff, H. (ed.), Bergische Universitat - Gesamthochschule Wuppertal, Wuppertal, Germany, pp VERHAGEN, H.J. (1996) Coastline Management, Volume 1. International Institute for Infrastructural, Hydraulic and Environmental Engineering (IHE), Delft, The Netherlands VERHAGEN, H.J. AND SAVOV, B. (2000) Sea Breeze Generated waves on the coast of Varna. Proceedings 2 nd International Conference Port Development and Coastal Development: PDCE 2000, Varna, Bulgaria WAVEBRAKE (2011) Modular floating breakwater. Available at [Accessed at March 13, 2011] WHISPRWAVE (2011) Modular floating breakwater. Available at [Accessed at March 13, 2011] WIEGEL, L.W. (1960) Transmission of waves past a rigid vertical thin barrier. Journal of the Waterways and Harbours Division, Vol. 86, pp WINDFINDER (2010) Wind statistics. Available at [Accessed at June 14, 2010] 147

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149 Figure references BING MAPS (2005) Available at [Accessed at May 11, 2010] GOOGLE EARTH (2010) Aerial photos of the earth [Accessed at May 11, 2010] GOOGLE MAPS (2010) Available at [Accessed at June 18, 2010] 149

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151 Appendix A Bathymetry survey In this appendix, the method of the bathymetric survey will be described. On September 14 and 15, 2010, a field investigation at the project location has been carried out. One of the tasks was obtaining detailed bathymetry data of the project location. The result of the bathymetric survey would be a detailed bathymetry map of the project site between the groynes and a larger overview map. The boundaries of these maps have been indicated in blue in Figure A.2. The equipment to obtain the bathymetric data where a rubber boat, a Fishfinder single beam echo sounder and a Garmin handheld GPS device. The track which has been sailed at September 14 has been displayed in green Figure A.2. As can be seen from this figure, a quite dense track has been sailed between the groynes. Further offshore, a less dense track has been sailed. During the sand sampling investigation at the September 15 the depth has also been measured. The track that has been sailed at this day is displayed in orange in Figure A.2. During both days, some water level set down occurred due to some wind blowing from the west. While at the project location, this set down was visible on the groynes (see Figure A.1). The estimation of the water level set down was 0.10 m. Also, the submergence of the echo sounder had to be taken into account. The submergence below the water level was 0.10 m. Furthermore, for the representation of position the coastline, a base map from the surroundings has been used. As can be seen, the sailed track does not cover the complete area within the large blue rectangle. To obtain full coverage of the area within the rectangle, the bathymetry map that has been obtained from the field research from SAVOV (2005) has been used as second data source. This map has been displayed on the background of Figure A.2. With red dots has been indicated which points have been added to the data set of the sailing tracks. Figure A.1: A water level set down of approximately 0.1 m is visible on the groyne. 151

152 Figure A.2: Bathymetry data sources: sailing tracks from 14 th (green) and 15 th (orange) of October and extra bathymetry points (red) taken from the bathymetry map from SAVOV (2005). The boundaries of the to be created large and detailed bathymetry maps have been indicated in blue. With the aid of the computer program Surfer 8, the two bathymetric maps have been created. These maps have been displayed in Section

153

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155 Appendix B Wind set-up calculation Below, the description of the calculation of wind set-up by CRESS (a programme with simple preprogrammed calculation rules) can be found. The text has been copied from the help file of CRESS (CRESS, 2010). Calculation of water level as a function of fetch length, water depth and wind speed. As extra parameters the approach angle towards the coast can be entered. The calculation is carried out in two steps. In the first step the rise in the deeper section is calculated. in the second step the calculation in a shallow section is calculated. The calculation is done for either open sea (lake/sea = 3) or for a closed lake (lake/sea = 1). Constants and parameters Included in the routine are the following constants: 1. air = 1.21 kg/m 3 2. water = 1030 kg/m 3 The friction factor c w varies between 0.8*10-3 and 3*10-3 (see CUR-CIRIA [1991], p190, which reference is based on Abraham, et al. [1979]). In this routine by default 2.72*10-3 is used, and consequently a value of = 3.2*10-6. Kamphuis [2000], p134 suggest that = 3.2*10-6 should be used. The Netherlands Delta Committee (Part IV) suggested = 3.4*10-6, Bretschneider suggested = 3*10-6. For canals a value of = 2*10-6 is recommended by Nortier. Equations used air cw (equation 1) water Basic equation for set-up is (see CUR-CIRIA [1991], p : dh dx 2 1 u cos gh According to some investigators the cos-function should be squared (see eg. Kamphuis [2000], p134). For a closed lake an extra coefficient 0.5 has to be included (because there is a set-down at the leeward side of the lake). 155

156 For a closed lake this results in: 2 u dh1 0.5 F cos gh (equation 2) In which: - u = wind velocity - h = water depth - F = fetch length - = approach angle to the coast (0 = perpendicular) For the open sea the following equation 3 is used. For a derivation of this equation is referred to Bretschneider [1966]. According to " Leidraad Rivierdijken II" this equation is valid for h/f <0.001): u (equation 3) g 2 2 ddh 2 F cos h h In this equation F is the fetch and h is the water depth. For the shallow part for a lake also equation 3 is used, but using different values for h and F (depth of shallow section and width of shallow section). For the shallow section at open shore line, equation 3 is used, in which F is the local fetch (= width of the shallow zone) and h is the depth of the shallow zone. The total set up is the sum of the deep water set-up and the shallow water set-up. Special comments All combinations of equation 2 and 3 are possible: Lake/sea Deep part Shallow part -1 eq 2. using 0.5 eq. 2, using eq 2, using 1.0 eq. 2, using eq. 2, using 0.5 eq. 3 2 eq.2, using 1.0 eq. 3 3 eq. 3 eq. 3 References - Bretschneider [1966] Engineering aspects of hurricane surge, in: T. Ippen, Estuary and coastline Hydrodynamics, McGraw-Hill, New York, pp Abraham, Karelse & Van Os [1979] The magnitude on interfacial shear of sub-critical stratified flows in relation to interfacial stability - Leidraad Rivierdijken II [1989] Technische Adviescommissie voor de Waterkeringen - CUR-CIRIA [1992] Manual on the use of rock in Hydraulic engineering - Kamphuis [2000] Introduction to coastal engineering and management, World Scientific, Singapore, ISBN , 437pp 156

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158

159 Direction Direction [ ] Significant wave height Hs [m] Zero-crossing period Tz [s] Peak period Tp [s] Wind speed [m/s] Probability of occurrence [%] Probability of occurrence [-] Probability of non-exceedance P [-] Probability of exceedance Q [-] Number of storms per year (storm duration is 30 hours) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Appendix C Wave climate C.1 Offshore wave climate Offshore wave climate Probabilities Northeast East Southeast South Northeast East Southeast South Northeast East Southeast South Northeast East Southeast South Northeast East East East Northeast East Southeast South Northeast East Southeast South Northeast

160 Direction Direction [ ] Significant wave height Hs [m] Zero-crossing period Tz [s] Peak period Tp [s] Wind speed [m/s] Probability of occurrence [%] Probability of occurrence [-] Probability of non-exceedance P [-] Probability of exceedance Q [-] Number of storms per year (storm duration is 30 hours) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Offshore wave climate Probabilities East Southeast South Northeast East Northeast East Southeast South Northeast East Southeast South Northeast East East Northeast East Northeast East East Northeast East East East East

161 C.2 Near shore wave climate 161

162

163 Appendix D Sediment sample analysis D.1 Field research On the September15, 2010 several sand samples have been taken near the project location and at several locations offshore from the project location. With the aid of a diver the sand samples were taken. The instrument used to collect the samples was a so called piston sampler. This instrument consists of two steel tubes inside each other. One tube can be pushed into the soil to obtain a sample. With this instrument, sediment samples were obtained to a depth of maximum 2 m below the sea bed. As base to make a plan on which locations to take samples, the field research of SAVOV (2005) has been taken. In Figure D.1 map of the surroundings of the project location has been displayed. In this map an underlay with sediment layer thickness and 39 sample locations has been displayed. These data are the result of the field research from The sand layer thickness has been measured with the aid of a steel rod. Sediment samples have been taken from the surface of the sea bed. The layer thickness data have been used to determine suitable sampling locations for the field research in The sampling locations of 2010 have been indicated in Figure D.1 with the symbol and a caption. Figure D.1: Locations of the sand samples that have been taken. The contour map displays the sand layer thickness in m, as measured by SAVOV (2005). 163

164 At 13 locations samples have been taken. - 4 samples have been taken between the groynes to determine the properties of the native sand near the shore, namely: A3 A2 213 C1-7 samples have been taken in the area where most of the samples have been taken during the research of SAVOV (2005). As can be seen from the underlay, more to the east the thickness of the layer is larger than to the west. That s why more samples have been taken to the east than to the west. The numbers of these samples are: One sample has been taken far offshore, to see if the material far offshore is different from the material more near shore, namely: 272 After a sample was taken from the bottom, the piston sampler was emptied in a bucket. Next, the sample was stirred and some material was put in a plastic bag. Later, the samples have been dried until the water was evaporated from the sample. After this, a description of the samples has been given and pictures of the samples have been taken. D.2 Method to determine sieve curves In the Geotechnical Laboratory in the Faculty of Civil Engineering and Geosciences of TU Delft, the sand samples have been analysed. The sieve curves of the samples will be obtained by means of a hydrometer test. The method to be followed is described in MULDER AND VERWAAL (2006). By following this manual, the test will be carried out in accordance with the following standard: BS 1377: part 2: 1990 (BS stands for British Standard Institution). In this section, a description of the method of analysis will be given. D.2.1 Scope of the test The hydrometer analysis is a widely used method to obtain the distribution of particle sizes in the silt range (63-2 μm), and the percentage of clay materials (< 2 μm). The test is usually not performed if less than 10% of the material passes the 63 μm sieve. The hydrometer analysis utilises the relationship among the velocity of fall of spheres in a fluid, the diameter of the sphere the specific weights of the sphere and of the fluid and the viscosity of the fluid as expressed by Stokes law (Cited from MULDER AND VERWAAL, 2006). 164

165 D.2.2 Equipment used soil hydrometer, see Figure D.2: Figure D.2: Soil hydrometer (left) and hydrometer floating in glass sedimentation cylinder (right).: two 1000 ml glass measuring cylinders, with rubber stops thermometer high speed stirrer sieves for dry sieving: mm 0.15 mm 0.3 mm 0.6 mm 1.18 mm 2 mm 3.35 mm receiver sieving machine, see Figure D.3: 165

166 Figure D.3: Sieving machine with sieves and receiver. sieve for wet sieving: mm balance readable to 0.01 g drying oven set at C D.2.3 Preparations stopwatch readable to 1 s steel rule evaporating dishes (for during in oven) measuring cylinder of 100 ml wash bottle and distilled water constant temperature bath standard dispersant solution: that is 33 g of sodium hexametaphosphate and 7 g sodium carbonate in distilled water to make a 1 litre solution. Calibrations and corrections of hydrometer readings Each density reading taken on the hydrometer must first be expressed as a hydrometer reading, R h, corresponding to the level of the upper rim of the meniscus. This is done by subtracting 1 from the density and moving the decimal point three places to the right. For example, a density of would be a hydrometer reading of R h = 28. Meniscus correction - Insert the hydrometer in a 1 litre cylinder containing about 800 ml water - By placing the eye slightly below the plane of surface of the liquid and then raising it slowly until the surface seen as an ellipse becomes a straight line, determine the point where the plane intersects the hydrometer scale. 166

167 - By placing the eye slightly above the plane of surface of the liquid, determine the point where the plane intersects the hydrometer scale. - Record the difference between the two readings as the meniscus correction, C m, expressed as: R R C ' h h m (Cited from MULDER AND VERWAAL, 2006) D.2.4 Scale calibration of the hydrometer Before executing the measurements, a scale calibration of the hydrometer has to be performed. Calculate the effective depth, H R (mm), corresponding to each of the major calibration marks, R h, from the equation: V 1 h H R H 2 h L 900 Where: H R = effective depth [mm] H = length from the neck of the bulb to gradation R h [mm] h = length of the bulb [mm] = 159 mm for B.S. (=British Standard) hydrometer L = distance between the 100 ml and the 1000 ml scale markings of the sedimentation cylinder (Cited from MULDER AND VERWAAL, 2006) In Figure D.4, the above mentioned parameters have been clarified. Figure D.4: Calibration of a hydrometer 167

168 Three different sedimentation cylinders have been used, so three calibrations have been performed. The cylinders have been numbered 1, 2, and 6. The only parameter that was different for each of the calibrations, was the value of L, the distance between the 100 ml and the 1000 ml scale markings of the sedimentation cylinder. On the following pages, the calibration results have been displayed. 168

169 169

170 170

171 171

172 D.2.5 Execution of the test The following steps have been undertaken to analyse the dried soil samples as they have been brought back from Bulgaria: Dispersion - Take approximately 100 g of each soil sample and weight the sample to 0.01 g. This is the start mass of the sample. - Add 100 ml of the standard dispersion solution to the soil. - Shake the mixture thoroughly until all the soil is in suspension. - Transfer the soil with some distilled water to the cup of the high-speed stirrer and stir for about 1 hour. - Transfer the suspension to the mm sieve placed on a receiver. - Wash the soil in the sieve with a maximum of 500 ml distilled water. - Transfer the suspension in the receiver into a 1000 ml sedimentation cylinder, this will be the sedimentation cylinder. - Transfer the material retained on the mm sieve to an evaporating dish and dry it in the oven at 105 to 110 C. - When cooled, sieve this material on the mm, 0.15 mm, 0.3 mm, 0.6 mm, 1.18 mm, 2 mm and 3.35 mm sieves. - Dry and weigh the material retained on each sieve to 0.01 g. - Add any material passing the mm sieve to the sedimentation cylinder. (Cited from MULDER AND VERWAAL, 2006) Sedimentation - Fill the sedimentation cylinder to the 1000 ml gradation mark with distilled water. - Place the sedimentation cylinder in the constant temperature bath, set on 25 C. - Place a second cylinder containing 100 ml of the dispersant solution and distilled water to exactly 1000 ml in the constant temperature bath: this is for holding the hydrometer between the readings. - Allow the cylinders to stand in the bath until they reached the bath temperature (about 1 hour). - Insert s rubber stop in the sedimentation cylinder or close it off by hand and shake the cylinder vigorously to obtain a uniform. suspension. Stir if necessary with a glass rod so that all material goes into suspension. The cylinder is inverted for a few seconds, and then put in the constant temperature bath. Without delay, as soon as the cylinder is in upright position, the stopwatch is started (zero time). - Remove the rubber stop from the sedimentation cylinder and insert the hydrometer steadily and allow it to float freely. It must not be allowed to bulb up and down, or to rotate. However, a quick rotational twist with the fingers on the top of the hydrometer will dislodge any air bubbles which may adhere to the side. - Readings of the hydrometer are taken at the top of the meniscus level at the following times from zero: 0.5, 1, 2 and 4 minutes. - The hydrometer is removed slowly, rinsed in distilled water, and placed in the separate cylinder of distilled water in the constant temperature bath. - Observe and record the top of the meniscus reading, R 0. - Insert the hydrometer for further readings at the following times from zero: 8, 30 minutes, 2, 8 and 24 hours. It is not essential to keep rigidly these times, provided that the actual time of each reading is recorded. insert the hydrometer slowly about 15 s before a reading is due. 172

173 - Insert and withdraw the hydrometer very carefully to avoid disturbing the suspension unnecessarily. - Observe and record the temperature of the bath after every recording. Of the temperature varies more than 1 C, another reading to determine R 0 should be taken. (Cited from MULDER AND VERWAAL, 2006) D.2.6 Density measurements For the calculations that have to be done to obtain the sieve curves of the samples, the density of the grain material itself has to be obtained. The density has been obtained by means of an automatic gas pycnometer. The pycnometer used has been displayed in Figure D.5. This device uses the principle of Archimedes and Boyle s law to determine the volume of a certain amount of soil that will be inserted in the pycnometer. First, some soil has to be put in a little cup that fits inside the pycnometer. The amount of soil that has been put in the cup is weighted before putting it in the pycnometer. When the cup with soil is inserted in the device, the density will be determined by the pycnometer. The device does this by means of pumping helium gas in the soil until a certain target pressure is reached. The amount of gas that has been pumped in the cup is measured. Boyle s law describes the inversely proportional relationship between the absolute pressure and volume of a gas, if the temperature is kept constant within a closed system. By means of this law, the pycnometer can calculate the volume of the pores inside the soil, by means of measuring the initial pressure and the amount of gas that has been pumped in the soil to achieve a certain target pressure. Because the volume of the cup is known, the volume of soil can be calculated by subtracting the calculated pore volume from the volume of the cup. By means of the weight of the sample and the volume of the grains, the pycnometer can calculate the density of the material of the grains. Figure D.5: Automatic gas pycnometer. In total 12 samples have been obtained. However, to get an impression of the density of the grain material, the density of only 7 samples has been determined. The results of the density measurements have been summarized in 173

174 Table D.1. As can be seen, all the measured densities have values around 2700 Mg/m 3. That s why the choice has been made to use the average value of the calculated densities as representative value for all the samples that have been taken. This mean value is kg/m 3, as can be seen in the last row of Table D.1. Table D.1: Results of density measurements. The density values have also been given in Mg/m3, because that s the unit that has to be used in the formulas given below. Sample Density [Mg/m 3 ] Density [kg/m 3 ] A Average D.2.7 Calculation Dispersion Calculate the percentage off mass passing each sieve, by using the start mass of the sample. Sedimentation - Calculate the effective depth H r, wit the aid of the relation obtained during the hydrometer calibration. - Calculate the equivalent particle diameter D for each density reading, from the equation: H r D s 1t Where: D = equivalent particle diameter [mm] η = dynamic viscosity of water at the test temperature [mpa.s] H r = effective depth [mm] ρ s = particle density [Mg/m 3 ], as determined with the aid of the pycnometer t = elapsed time [min] - Calculate the modified hydrometer reading, R d, from the equation: R R R d ' h ' 0 Where: R d = modified hydrometer reading R h = hydrometer reading at the upper rim of the meniscus in the sedimentation cylinder R 0 = hydrometer reading at the upper rim of the meniscus in the dispersant solution 174

175 - Calculate the percentage by mass, K, of the particles smaller than the corresponding equivalent particle diameter, D [mm], from the equation Where: K ρ s m R d 100s K ms 1 R = percentage by mass of the particles smaller than the corresponding equivalent particle diameter D = particle density [Mg/m 3 ], as determined with the aid of the pycnometer = start mass of the dry sample [g] = modified hydrometer reading (Cited from MULDER AND VERWAAL, 2006) Sieve curve The calculation results from both the dispersion and the sedimentation can now be combined to obtain the sieve curve of the sample. d D.3 Results regarding sieve curves In this section the results of the sediment sample analysis will be presented. On the next pages, the results per sample will be displayed. The following information per sample will be presented: 1. A picture of the dried sample. 2. The location where the sample has been taken indicated on a map, including UTM coordinates of the location. 3. A picture of the fraction of the sample with grains larger then mm. 4. A description of the sample right after drying 5. The sieve curve in graphical format. 6. From this sieve curve, an estimation will be made of the mean grain diameter D 50 of the sample. 7. The value of D 85 /D 15, which is a measure of how uniform the material in the sample is distributed. 8. The percentage of fine material (smaller then mm) in the sample. 9. The hydrometer density measurements. 175

176 D.3.1 Near shore samples Sample A3 Location: m East, m North Sample after drying Location Part of sample with grains larger then mm Description of the sample right after drying Number Description of material Remarks regarding shell parts and other bigger particles A3 Sandy, no cohesion Crushed small shell parts, shells have the size of grains Estimated shell size [mm] 0.18 (size of grains) 176

177 177

178 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Hydrometer test A Grain size (mm) Sieve curve Summary of test results D 50 [mm] D 85 [mm] D 15 [mm] D 85 /D 15 [-] Percentage of fines [%]

179 Sample A2 Location: m East, m North Sample after drying Location Part of sample with grains larger then mm Description of the sample right after drying Number Description of material Remarks regarding shell parts and other bigger particles A2 Sandy, no cohesion Crushed small shell parts, shells have the size of grains Estimated shell size [mm] 0.18 (size of grains) 179

180 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Hydrometer test A Grain size (mm) Sieve curve Summary of test results D 50 [mm] D 85 [mm] D 15 [mm] D 85 /D 15 [-] Percentage of fines [%]

181 181

182 Sample 213 Location: m East, m North Sample after drying Location Part of sample with grains larger then mm Description of the sample right after drying Number Description of material Remarks regarding shell parts and other bigger particles 213 Little cohesion Almost no shells 1-2 Estimated shell size [mm] 182

183 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Hydrometer test Grain size (mm) Sieve curve Summary of test results D 50 [mm] D 85 [mm] D 15 [mm] D 85 /D 15 [-] Percentage of fines [%]

184 184

185 Sample C1 Location: m East, m North Sample after drying Location Part of sample with grains larger then mm Number Description of material Remarks regarding shell parts and other bigger particles C1 Sandy, no cohesion Crushed small shell parts 2 Description of the sample right after drying Estimated shell size [mm] 185

186 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Hydrometer test C Grain size (mm) Sieve curve Summary of test results D 50 [mm] D 85 [mm] D 15 [mm] D 85 /D 15 [-] Percentage of fines [%]

187 187

188 D.3.2 Offshore samples Sample 1 Location: m East, m North Sample after drying Location Part of sample with grains larger then mm Description of the sample right after drying Number Description of material Remarks regarding shell parts and other bigger particles 1 Quite hard, lot of cohesion, sandy, some clay Very few shells, some unidentified coarser particles, stones ceramic parts Estimated shell size [mm]

189 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Hydrometer test Grain size (mm) Sieve curve Summary of test results D 50 [mm] D 85 [mm] D 15 [mm] D 85 /D 15 [-] Percentage of fines [%]

190 190

191 Sample 5 Location: m East, m North Sample after drying Location Part of sample with grains larger then mm Description of the sample right after drying Number Description of material Remarks regarding shell parts and other bigger particles 5 Sandy, lot of cohesion Not many shells 1-5 Estimated shell size [mm] 191

192 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Hydrometer test Grain size (mm) Sieve curve Summary of test results D 50 [mm] D 85 [mm] D 15 [mm] D 85 /D 15 [-] Percentage of fines [%]

193 193

194 Sample 6 Location: m East, m North Sample after drying Location Part of sample with grains larger then mm Description of the sample right after drying Number Description of material Remarks regarding shell parts and other bigger particles 6 Sandy, some clay Little amount of shells 1-10 Estimated shell size [mm] 194

195 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Hydrometer test Grain size (mm) Sieve curve Summary of test results D 50 [mm] D 85 [mm] D 15 [mm] D 85 /D 15 [-] Percentage of fines [%]

196 196

197 Sample 9 Location: m East, m North Sample after drying Location Part of sample with grains larger then mm Description of the sample right after drying Number Description of material Remarks regarding shell parts and other bigger particles 9 Sandy, some clay Little amount of shells 1-10 Estimated shell size [mm] 197

198 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Hydrometer test Grain size (mm) Sieve curve Summary of test results D 50 [mm] D 85 [mm] D 15 [mm] D 85 /D 15 [-] Percentage of fines [%]

199 199

200 Sample 30 Location: m East, m North Sample after drying Location Part of sample with grains larger then mm Description of the sample right after drying Number Description of material Remarks regarding shell parts and other bigger particles 30 Sandy, some cohesion Lot of small shells of 1-2 mm, smaller amount of size 5-10 mm Estimated shell size [mm] 1-2 and

201 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Hydrometer test Grain size (mm) Sieve curve Summary of test results D 50 [mm] D 85 [mm] D 15 [mm] D 85 /D 15 [-] Percentage of fines [%]

202 202

203 Sample 32 Location: m East, m North Sample after drying Location Part of sample with grains larger then mm Description of the sample right after drying Number Description of material Remarks regarding shell parts and other bigger particles 32 Sandy, some clay Few larger ones 2-10 Estimated shell size [mm] 203

204 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Hydrometer test Grain size (mm) Sieve curve Summary of test results D 50 [mm] D 85 [mm] D 15 [mm] D 85 /D 15 [-] Percentage of fines [%]

205 205

206 Sample 160 Location: m East, m North Sample after drying Location Part of sample with grains larger then mm Description of the sample right after drying Number Description of material Remarks regarding shell parts and other bigger particles 160 Sandy, some clay Little amount of shells 1-10 Estimated shell size [mm] 206

207 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Hydrometer test Grain size (mm) Sieve curve Summary of test results D 50 [mm] D 85 [mm] D 15 [mm] D 85 /D 15 [-] Percentage of fines [%]

208 208

209 D.3.3 Offshore samples Sample 272 Location: m East, m North Sample after drying Location Part of sample with grains larger then mm Description of the sample right after drying Number Description of material Remarks regarding shell parts and other bigger particles 272 Sandy silt, very cohesive Fine shells, not many Estimated shell size [mm] 209

210 Percentage passing (%) Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Hydrometer test Grain size (mm) Sieve curve Summary of test results D 50 [mm] D 85 [mm] D 15 [mm] D 85 /D 15 [-] Percentage of fines [%]

211 211

212 D.4 Determination of amount of calcium carbonate D.4.1 Method At January 31, 2011, the amount of calcium carbonate has been determined in a laboratory of the Department of Geotechnology of Delft University of Technology. The report with the results (in Dutch) can be found in Appendix D.4.3. To get an indication of the amount of calcium carbonate in the area, two samples have been analysed. The numbers of the samples are 5 and 32. The locations of the samples have been indicated in the map of Figure D.6. Figure D.6: Locations of the samples that have been analysed (5 and 32). The method that has been used to determine the amount of calcium carbonate, is the titrimetric method by Rowell (reference: see Section D.4.3). The method is a two phase analysis: - The soil is mixed with a known amount of HCl. The carbonate will be dissolved by the following balance equation: CaCO HCl Ca Cl - + H 2 O + CO 2 - De amount of acid that remains after the reaction is measured by titration with NaOH. Depending on the homogeneity of the sample that has to be analysed, at least two sub samples per sample will be taken. If the results of the two analysed sub samples differ more then 5%, a third sub sample will be analysed. The total time of analysis amounts approximately 30 minutes. 212

213 D.4.2 Results Samples 5 and 32 have been analysed. The samples have been dried and delivered to the laboratory with a grain size smaller than 2 mm. The results can be found in the following table: Sample 5 (1) 5 (2) 32 (1) 32 (2) % CaCO , ,5 (1) = sub sample 1 (2) = sub sample 2 The amount of calcium carbonate in sample 5 amounts 41 %. The amount of calcium carbonate in sample 32 amounts 52 %. 213

214 D.4.3 Laboratory report (in Dutch) (INTERN) ANALYSERAPPORT TA Opdrachtgever: H.J. Verhagen / R. Drieman (contactpersoon: H.J.Verhagen@tudelft.nl) Baancode: C71947/2011 Uitgevoerd door: J. van Haagen (J.vanHaagen@tudelft.nl) Datum uitvoering: 31 januari 2011 Bepaling van het carbonaatgehalte in zandmonsters Methode: titrimetrische methode volgens Rowell (1994) 1. De methode is een twee-fase analyse: 1. De grond wordt gemengd met een bekende hoeveelheid HCl en hierdoor wordt het carbonaat opgelost volgens: CaCO HCl Ca Cl - + H 2 O + CO 2 2. De hoeveelheid zuur die na reactie overblijft wordt gemeten door titratie met NaOH. Afhankelijk van de homogeniteit van het te analyseren monster worden er minimaal 2 deelmonsters per monster genomen. Als de resultaten meer dan 5% uit elkaar liggen wordt nog een derde deelmonster geanalyseerd. Totale analysetijd per deelmonster: ca. 30 minuten. Resultaten: Monster no. 5 en monster no. 32 zijn geanalyseerd. De monsters zijn gedroogd en met korrelgrootte < 2mm aangeleverd. monster 5 (1) 5 (2) 32 (1) 32 (2) % CaCO , ,5 (1) = deelmonster 1 (2) = deelmonster 2 Het carbonaatgehalte in monster 5 bedraagt 41 % Het carbonaatgehalte in monster 32 bedraagt 52 % 1 Rowell, D.L. (1994) Soil Science: Methods and Applications. Harlow, Longman Scientific and Technical. ISBN:

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217 Appendix E Sediment fall velocity calculation Below, the description of the calculation of the sediment fall velocity by CRESS (a programme with simple pre-programmed calculation rules) can be found. The text has been copied from the help file of CRESS (CRESS, 2010). In this rule some general parameters of water and sediment are calculated: - Viscosity of water - Density of water - Settling of sediment - Shields number - Van Rijns sedimentological diameter and Shields number The equations are mainly based on the book of Van Rijn and the scour manual. The equations for density of sea water, the viscosity are based on curve-fitting of experimental results, mainly of tests by Delft Hydraulics and Utrecht University. Input parameters: - S = salinity in parts per thousand of per mille ( ) - T = temperature in C - D 50 = median grain size [in the input screen of the rule values should be entered in microns, in the equations below S.I.-units are used (thus D 50 in m)] Density of sea water: 2 w S T S 0.03 Kinematic viscosity: Dynamic viscosity: T T Relative density: s w w 217

218 Settling velocity: W W gd for D m gD 1 for m m D 2 50 D 50 W gd D for m [ ] References - Van Rijn, Hoffmans & Verhey, Scour manual Schiereck, G.J. [2001] - Introduction to bed, bank and shoreline protection, Delft University Press, ISBN

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221 Feasibility study on the use of a floating breakwater to protect a new artificial beach in Balchik, Bulgaria Appendix F Longshore transport calculation 221

222 Total longshore sediment transport rates (results of column 23) Total pos. Total neg. Total [m 3 /year] [m 3 /year] [m 3 /year] Total amount of sediment that passes groynes (results of column 28) Passed west Passed east Total passed groynes [m 3 /year] [m 3 /year] [m 3 /year]

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225 Appendix G Calculation of breaker depth and refraction Below, the description of the calculation of the breaker depth, shoaling coefficient, refraction coefficient, significant wave height at the point of breaking and the angle of wave incidence at the point of breaking by CRESS (a programme with simple pre-programmed calculation rules) can be found. The text has been copied from the help file of CRESS (CRESS, 2010). Short description This rule calculates the changes of linear waves near coasts with parallel depth contours Used equations Deep-water wavelength and shallow water wavelength are calculated with the standard approximations used by Cress (see rule z10: orbital movement). The shoaling coefficient can be calculated directly: K s 1 2h b 2 hb tanh 1 L 2 h b L sinh L 15 (equation 1) The direction of the wave is given by: L 1 arcsin sin0 L0 (equation 2) The refraction coefficient is given by: K r cos cos 0 (equation 3) 1 The wave height at breaking is: H H K K (equation 4) b 0 s r Additionally breaking takes place at the point where: H h b b (equation 5) 225

226 An iteration procedure starts at a depth of 3 times H 0 and moves towards the coastline. As soon as the breaker-criterion is met, iteration stops. The breaker index (sometimes called breaker parameter) is used as input. For single (solitary) waves one should use a value of For random waves (calculation on the basis of H s ) one should use a value of 0.4 to 0.5. [ ] References Kamphuis, J.W. [2000] Introduction to coastal engineering and management. Advances Series on Ocean Engineering, Vol. 16, World Scientific, Singapore, ISBN or (pbk) 226

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229 Appendix H Visit Ship Machine Building At the September 21, 2010 the company Ship Machine Building has been visited to investigate the possibilities to produce the floating breakwater. Ship Machine Building is a company in Varna, Bulgaria which has specialized itself in producing floating structures made of Ferro concrete. Ship Machine Building has a wharf available with two slipways, see Figure H.1. The answers to the questions that have been asked during the visit can be found hereafter. What are the maximum possible dimensions of a structure that can be build? The maximum dimensions of a structure that can be build on a slipway is length x width = 95 m x 19 m. The depth of the water next of the slipway amounts 4.7 m, so this has to be taken into account when calculating the draft of the structure. The maximum weight of a structure to be created can be 1200 t. What is the density of the concrete used? Figure H.1: The two slipways of Ship Machine Building The density of the concrete used by Ship Machine Building is 2400 kg/m 3. The compartments of the concrete structure can be filled with a foam material which has a density of kg/m 3. What wall thicknesses are used to create concrete floating structures? An example of a structure built by Ship Machine Building had a deck of 8 cm thickness and a bottom of 10 cm thickness. The concrete coverage on the steel reinforcement bars amounts 1.5 cm on the outside and 1 cm on the inside. What could the lifetime of the structure be? One concrete hull that has been constructed by Ship Machine Building has been in salt water since This hull is still in good shape and undamaged. That means that the structure has been undamaged for 33 years. This gives an indication that Ferro concrete is a very good and resistant material to the use in water. What is the possible production rate at Ship Machine Building? Production rates of 150 m 3 of concrete per day have been reached in the past. One time 330 m 3 of concrete had been poured without a break. 229

230 What about the costs of a concrete structure? The floating ramp displayed in Figure H.2 has been constructed by Ship Machine Building. The amount of concrete used to construct this ramp is 330 m 3. The price to buy the ramp from Ship Machine Building amounts 300,000. A first assumption for the construction costs per m 3 of concrete can therefore be 300,000 / 330 m 3 = 909 / m 3. Figure H.2: Floating ramp built by Ship Machine Building. 230

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233 Appendix I Types of floating breakwaters In this appendix, an investigation will be made regarding possible types of floating breakwaters. Positive and negative aspects of each type will be described. I.1 Classification of floating breakwaters Because of the fact that there are many of types of floating breakwaters, it is practical to classify them in a certain way. PIANC (1994) is a practical report on the design of floating breakwaters. In this report a classification regarding the way the breakwater attenuates incident waves is given regarding the way they attenuate incoming waves: - Reflective structures: the main effect of this type is that incident waves are reflected, so that only a part of the wave energy passes the breakwater. This has been illustrated in Figure I.1a. - Dissipative structures: the main effect of this type is that incident wave energy is dissipated via friction, turbulence, etc. This has been illustrated in Figure I.1b. a b Figure I.1: Reflective (a) and dissipative (b) floating breakwaters. H I is the incident wave height, H T is the transmitted wave height and H R is the reflected wave height (PIANC, 1994). This classification is arbitrary, since each floating breakwater type partially functions in both ways. However, the classification is adopted to categorize the several types of floating breakwaters that will be given in Section I.2. I.2 Types of floating breakwaters In this section, several types of floating breakwaters will be described. Distinction is made between reflective and dissipative systems. In PIANC (1994) many examples are given. This overview will be further extended in this section. I.2.1 Reflective types Single pontoon with rectangular cross section The most common used floating breakwater type is the single pontoon with a rectangular crosssection. These pontoons are often made of concrete or reinforced concrete. The hollow part of the pontoons can be filled with floatation material, such as expanded polystyrene (EPS). The pontoons are bounded by piles that are driven into the soil or, more often, attached to the sea floor via mooring lines. 233

234 Figure I.2: Single pontoon breakwater (PIANC, 1994) A schematic cross-section of a singe pontoon floating breakwater can be seen in Figure I.2. The water depth is indicated by d. Incoming waves are characterised by the wave height H and the wave period T. Via the wave period T they are also characterised by the wave length L. The dimensions of the breakwater itself are width W and height h. Mechanical properties of the breakwater are the height of the centre of gravity h G, the mass M and the moment of inertia I. Important dimensionless parameters governing the wave attenuation capacity are believed to be the relative depth, d L, and the relative width, W L. The first one says something about the wave energy distribution in the water column. In literature, curves can be found presenting relationships between the wave transmission coefficient K T and these parameters. A typical shape of a curve giving the relation between K T and W L can be found in Figure I.3. Figure I.3: Relation between transmission coefficient (in this figure called C T ) and relative width (adapted from PIANC (1994)). The agreement between theory and experiments is quite good, except for cases near resonance. The resonance can be seen in the graph where the theoretical K T value is zero. The difference between the graphs can be attributed to the fact that as soon as motions become predominant (resonance) the theoretical linear model is no longer valid. Also, purely regular waves and perfect elastic mooring systems do not exist, even in wave tanks. That s why resonance can never be as sharp as predicted by the model. Also, reference could be made to the Dutch company FDN Engineering, which performed a lot of research to floating caisson type breakwaters. Double pontoon Another way of using pontoons is using two pontoons in series, connected to each other. In this way the moment of inertia can be increased, without increasing the total mass (OFUYA, 1968). A cross section of such a breakwater can be found in Figure I

235 Figure I.4: Double pontoon floating breakwater (PIANC, 1994). A double pontoon breakwater functions in the same way as a single pontoon, but in addition waves are attenuated by the generation of turbulence between the floating bodies. Other types of double pontoon breakwaters are: - Catamaran type breakwater. Such a type has been studied for Oak Harbour, Washington, USA. The cross-section of this breakwater can be seen in Figure I.5. The stability of this type of breakwater has been increased by concentrating the mass at a low level under the waterline. Figure I.5: Catamaran type floating breakwater (PIANC, 1994). - Alaska type or ladder type floating breakwater. This type of breakwater can be found in Figure I.6. It consists of two long concrete pontoons, with in between concrete connections. The first Alaska type breakwater has been built in Tenakee Springs, Alaska. Figure I.6: Alaska type floating breakwater (PIANC, 1994). - Canadian A-frame, see Figure I.7. It has a wall in the middle, which reflects part of the waves back in seaward direction. 235

236 Hinged floating breakwater Figure I.7: Canadian A-frame (PIANC, 1994). The hinged floating breakwater is a wall that has been hinged to the sea bottom (see Figure I.8). The wall extends through the entire water depth. This screen is moved by incoming waves. Restoring forces are the buoyancy of the structure and from mooring lines. In LEACH et al. (1985) a research on the hinged floating breakwater has been described. A theoretical model has been developed on the performance of the breakwater. This theoretical model has been verified by tests. In the paper graphs to determine the transmission coefficient have been given. Figure I.8: Hinged floating breakwater (PIANC, 1994). I.2.2 Dissipative types Tethered-float breakwater In Figure I.9 a so-called tethered float breakwater has been displayed. It consists of a series of independent floats moored to the sea bottom. The mooring lines are always in tension, because the floats have high buoyancy. The line length is equal to or a little less than the water depth. The system acts more or less the same as an inverted pendulum. The natural period of oscillation T 0 is proportional to the square root of the mooring line length. When the incident wave has a period which is close to T 0, the breakwater tends to oscillate out of phase with the incident wave. The velocity of water particles relative to the floats may become rather important in such a case. It can be assumed that the energy losses are proportional to u 3, in which u is the particle velocity. 236

237 Flexible membranes Figure I.9: Tethered-float breakwater (PIANC, 1994). It is possible to use flexible membranes as wave attenuators. The principle is based on a flexible membrane floating on or just beneath the water surface. In this case the membranes position is horizontal. It is also possible to place the membrane in a vertical position. In this case the membrane acts as a sort of vertical wall which interrupts the wave propagation. Holes can be present in the membrane to increase turbulence generation. In literature numerous investigations (theoretical, numerical and physical models) on the performance of flexible membranes can be found. Porous walled breakwater A type of breakwater that is designed to transform wave energy into turbulence is the porous walled floating breakwater, see Figure I.10. Partially the waves are attenuated by generation of turbulence. The remaining attenuation is caused by water level oscillation inside the structure. Floating tire breakwaters Figure I.10: Porous walled breakwater (PIANC, 1994). It is possible to create floating breakwaters with floating truck tires. Sometimes the tires are filled with flotation material such as polystyrene or polyurethane. Several types have been designed and patented. Some types exist purely of tires, such as the Goodyear module (Figure I.11a). Other types are constructed in combination with poles or beams, like the Pole-Tire (Figure I.11b). a b Figure I.11: Two types of floating tire breakwaters, the Goodyear Module (a) and the Pole Tire breakwater (b) (PIANC, 1994). The wave attenuation takes place in three ways. First, they serve partly as a reflective system. Second, the breakwater forms a semi-flexible sheet that tends to follow the motion of the water surface. If wave lengths are short and the structure itself is rigid enough, the sheet will reduce vertical 237

238 surface displacements. A third way the breakwater attenuates the waves is that its porosity generates drag forces, which contributes to energy losses. Because the structure has a small draft, it solely acts on the flow characteristics in the upper part of the water column. For this reason, tire breakwaters are only effective in greater water depths or where the wave energy is not equally spread over the water depth (PIANC, 1994). Modular floating breakwaters Another type of floating breakwater is the so called modular floating breakwater. These breakwaters consist of special shaped plastic modules which are connected to each other. Several types have been developed and patented, such as the WhisprWave and the Wavebrake of Florida (WHISPRWAVE, 2011 and WAVEBRAKE, 2011), see Figure I.12. a b Figure I.12: Examples of modular floating breakwaters, the WhisprWave (a) and the Wavebrake of Florida (b) (WHISPRWAVE, 2011 and WAVEBRAKE, 2011). Modular floating breakwaters dissipate wave energy by means of channelling the flow of water trough the holes and voids between the linked modules. While flowing trough the voids, energy will be dissipated by hydraulic resistance and friction. The modules will change the laminar flow of water into turbulent water motion (WAVEBRAKE, 2011). A brochure on the website of WhisprWave states that at the installation of WhisprWave elements at a marina in the USA, a transmission coefficient of 0.1 on the expected incoming wave spectrum was observed during a storm (WHISPRWAVE, 2011). Pneumatic and hydraulic breakwaters OFUYA (1968) gives a description about pneumatic and hydraulic breakwaters, see Figure I.13. Figure I.13: A pneumatic and a hydraulic breakwater (OFUYA, 1968). 238

239 Pneumatic and hydraulic breakwaters attenuate waves by means of air or water jets. These jets are directed upwards from locations below the water surface. Currents generated by the air or water jets cause incoming waves to get steeper and cause the waves to break. I.3 Further reading If one would like to know more about floating breakwaters in general, the different types of floating breakwaters and the performance of the different types of floating breakwaters, the following references give a good overview: - HALES, Z.L. (1981) Floating Breakwaters: State-of-the-Art Literature Review. U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Technical Report No. 81-1, Fort Belvoir, Virginia, USA - KATOH, J. (1992) Assessment of Floating Breakwaters. Marine Behaviour and Physiology, Vol. 20, Issue 1-4, pp OFUYA, A.O. (1968) On floating breakwaters. C.E. Research Report No. 60, Department of Civil Engineering, Queens University, Kingston, Ontario, Canada - PIANC (1994) Floating Breakwaters; A Practical Guide for Design and Construction. PTC II, Report of Working Group no. 13, Supplement to Bulletin 85, Permanent International Association of Navigation Congresses (PIANC) - TOLBA, E.R.A.S. (1999) Teil 1: Behaviour of Floating Breakwaters under Wave Action. In: Fachbereich Bauingenieurswesen, Lehr und Forschungsgebiet Wasserbau und Wasserwirtschaft, Bericht Nr. 11, Kaldenhoff, H. (ed.), Bergische Universitat - Gesamthochschule Wuppertal, Wuppertal, Germany, pp

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241 Appendix J Breakwat calculations of overtopping and required freeboard J.1 Overtopping and required freeboard Below, the description of the calculation of the needed freeboard to minimize overtopping over the floating breakwater by Breakwat (a programme with pre-programmed calculation rules on breakwater design) can be found. The text has been copied from the help file of Breakwat (BREAKWAT, 2005). The section numbers in the text below refer to section numbers in the help file of Breakwat. [ ] 3.6 Vertical (caisson) breakwaters For a vertical (caisson) type breakwater many advances have been made in recent years in order to compute the wave overtopping and wave forces on the structure. However, earlier works in Japan are often used as a basis, for comparison with newer studies. Most notable work is that one described in Goda (1985). For the calculation of pressures and forces on the structure this method assumes that no impulsive wave breaking occurs on the structure. This method cannot be used in such situations and if impulsive breaking may occur a warning message is issued to the user. For wave overtopping the graphs provided in Goda (1985) are based on the deep water wave height. However, nowadays it is common for the designer to know the wave height at the location of the structure. Van der Meer (2000) has made a review of many research studies on wave overtopping of vertical structures and has suggested a formula which reasonably describes the data sets analysed. This formula has therefore been incorporated. The following hydraulic response factors for vertical breakwaters can be computed with BREAKWAT: - Wave overtopping of vertical (caisson) breakwaters - Wave transmission over vertical (caisson) breakwaters The following structural response factors for vertical (caisson) breakwaters which can be computed with BREAKWAT are: - Pressures, forces and safety factors - Safety factors - Bearing pressures on foundation - Toe berm stability of vertical (caisson) breakwater [ ] 241

242 3.6.1 Hydraulic response factors Wave transmission over vertical (caisson) breakwaters The transmission of wave energy over a vertical structure can be described by the method of Goda et al. (1967). This formula included two coefficients, whose values depended on the type of structure. This formula is also used in the wave model SWAN and is described by: C C C t t t Rc 1 for H Rc 1 1 H si Rc 1 sin for 2 2 H si Rc 0.03 for H si si The transmitted wave height is defined as: H C H st t si in which α Coefficient depending on structure type (-) β Coefficient depending on structure type (-) H st Transmitted significant wave height (m) H si Incident significant wave height (m) R c Crest freeboard, vertical distance from MSL (m) The values of and must given as input. Typical values are defined as: - vertical (caisson) breakwater: α = 2.2; β = vertical wall (no crest width): α = 1.8; β = 0.10 [ ] 3.8 References - Goda, Y. (1985) Random seas and design of maritime structures. University of Tokyo Press, Japan. ISBN Goda, Y., Takeda, H. and Moriya, Y. (1967) Laboratory investigation of wave transmission over breakwaters. Rep. port and Harbour Res. Inst., 13 (from Seelig, 1979) - Van der Meer, J.W. (2000) Crest height of structures - methods. Infram publication nr. i336 (in Dutch) 242

243 J.2 Wave force Below, the description of the calculation of the wave force exerted on the side of the floating breakwater by Breakwat can be found. The text has been copied from the help file of Breakwat (BREAKWAT, 2005). The section numbers in the text below refer to section numbers in the help file of Breakwat Pressures, forces and safety factors Pressures Forces and Safety Factors against sliding and overturning of a vertical caisson are computed following the method described by Goda (1985). It is assumed that the shape of the caisson, with or without a vertical parapet wall on the front side. The purpose of a vertical parapet is to reduce the amount of wave overtopping. When a vertical parapet wall is present, the horizontal force on the caisson will increase but the amount of overtopping water will decrease. To maintain adequate safety factors the width or weight of the caisson will have to be increased compared to the situation without a wall. Figure 28 Definition sketch for vertical (caisson) breakwater The calculation procedure assumes that the wave height offshore of the structure (H s0 ) is known and a simple procedure is applied to estimate the wave height close to the structure, and therefore defining the design wave height (H D ). If the incident wave height (H si ) at the structure location is already known, then the user can adjust the offshore wave height such that the correct Hsi is obtained. This is described in more detail in Design wave height. For more background on the calculation of horizontal and vertical pressures, see Horizontal and vertical wave pressures and Bearing pressures on foundation. For more background on the calculation of safety factors, see Safety factors Horizontal and vertical wave pressures In this section the computation of the pressure distribution on the front face and underside of the caisson is described. The method of Goda (1985) is applied. However this method is however, not suitable for situations where impulsive breaking onto the caisson can occur - in those situations the peak wave pressures can be much higher than those computed with the Goda approach. Situations with impulsive breaking may occur for a certain combination of factors. In such cases a warning message is given, stating that impulsive breaking may occur and the results should be treated with caution. In such situations the pressures and forces should be evaluated by other methods. Technical background The elevation to which the horizontal wave pressure is exerted (measured from SWL) is * cos HD Wave pressures on the front of vertical wall: 243